Only one such incident was reported in 2012 and just one the following year.
But four close encounters were reported last year, and eleven this year so far.
In the first two weeks of this month alone, there were two incidents.
Not all the incidents proved drones were to blame - in some, reports could only establish that suspected unmanned aerial vehicles (UAVs) were sighted.
Digiflicks video producer Simon Baker, a UAV operator, said it was "just ridiculous" for anyone to fly a UAV near an aerodrome. "It's just nuts."
He said there were probably two reasons for the upsurge in reported near-misses.
Mr Baker said drone sales were increasing "exponentially" and the machines were in many cases getting cheaper.
He also said there was more public awareness of drones now.
Mr Baker said in some cases there was "hysteria" about drones but commercial drone operators took safety issues and near-misses seriously.
"I fly around myself in planes and don't want to be involved in something like that."
Steve Moore, CAA general aviation manager, cited the same two reasons for the rise in reported incidents.
He said birdstrikes and laser strikes remained far more common occurrences than UAV near-misses.
Mr Moore said the CAA's job was to ensure safety without "stifling" innovation.
"It's a really exciting area, and challenging as well."
He said a big challenge was educating people who weren't part of the traditional aviation scene.
Earlier this month, pilot and air traffic controllers' union NZALPA said all drones should immediately be "chipped", and have data plates or markings to make their owners or operators identifiable.
Mr Moore, however, said the CAA found microchipping drones would be impractical and in some cases draconian.
The CAA acknowledged drones had many useful roles, such as for real estate aerial photography and power lines inspection.
In one recent incident, an aircraft towing a glider last September took action to avoid what was described as a UAV.
In the most high-profile recent "near-miss", an Air New Zealand Airbus pilot reported a near-miss with a "circular red drone" five weeks ago.
No trace was found of the red drone reportedly involved, or its owner.
By law, drones under 25kg must only be flown in daylight, give way to all crewed aircraft, and stay below 400ft (120m).
Simon Roy Reeve, who has denied flying a Phantom 2 drone in controlled airspace in Pines Beach, will face a judge-alone trial on November 27 in Christchurch.
Today, police asked media not to use drones during the upcoming royal visit by Prince Charles and his wife Camilla.
Current and aspiring drone users are expected to gather at Wairarapa Drone Pilots' Drone Expo this weekend at the Clareville Complex near Carterton.
UFOs? UAVs? CLOSE ENCOUNTERS
• March 2012: People on a training flight see two UAVs "or a large model aircraft" flying nearby.
• November 2013: A six-seater plane near Riccarton reportedly comes close to a "UAV helicopter."
• September 2014: A pilot reports a near-miss with a suspected UAV about 20m away. The incident happened at 3100ft (945m) some 16km west of Claris, Great Barrier Island.
• September 2014: A glider takes evasive action due to a UAV. The UAV operator sees the glider towing earlier but doesn't realise the approach is across a motor racing track he's filming. He also hadn't contacted the aerodrome operator to discuss UAV flights.
• October 2014: Aircraft comes near two unmanned aircraft in the Foxton/Shannon training area. The aircraft gets within 500m horizontally and 61m vertically of the UAVs.
• November 2014: A helicopter 152m high has to avoid a large UAV.
• January 5, 2015: Crew of a helicopter fighting fires over Pines Beach, Canterbury raise concerns about an RPAS nearby.
• January 17: An aircraft comes close to "something that looked like a drone" while descending at 150m.
• February 6: A drone is seen at an altitude of 366m, to the right of a helicopter 100-150m away.
• February 15: A helicopter pilot sees a drone 150m away at 230m above ground, and takes avoiding action to avert collision.
• April 27: Crew of an unspecified aircraft report a near-miss with a drone flying at 790m.
• May 31: A UAV allegedly operates at about 150m, and 12m from a helicopter. Civil Aviation contacted the RPAS operator.
• July 30: A plane reportedly flies close to a UAV opearting area at Yaldhurst Quarry, Canterbury.
• September 8: In Otaki, a drone and aircraft come within 20m of each other. The drone opeartor was told to stop flying around Otaki airstrip.
• September 25: An Air New Zealand Airbus A320 reportedly comes close to a "sizeable" red RPAS above Christchurch.
• October 10: A small RPAS was near a Boeing 787 (Dreamliner) jet. Crew say the RPAS is orange and yellow and just to the jet's right-hand side.
• October 14: A suspected RPAS similar to a Parrot Quadrocopter is reportedly 90m away from a B200 approaching Ohakea.
