Mr Little was elected on November 18 after the resignation of David Cunliffe.
National's support rose 2.2 points, from 48.2 to 50.4 per cent in the poll, conducted in the second and third weeks of December.
On provisional election results, National won a majority of seats, but it lost that once special votes were counted. On final results, with 47.04 of the party vote and 60 seats, it formed a minority Government with its three previous support partners, Act, United Future and the Maori Party, and governs with 64 out of 121 votes.
Since the election, Prime Minister John Key has had mixed fortunes. He has attended Apec and the G20, and clinched a free-trade deal with South Korea.
But he has proposed sending training troops to the Middle East - an idea opposed by Labour - seen dairy prices plunge and forecasts of a surplus disappear, and been on the back foot after a damning report from the Inspector-General of Intelligence and Security, Cheryl Gwyn, who found the neutrality of the Security Intelligence Service had been compromised in its dealing with an Official Information Act request lodged by blogger Cameron Slater.
Mr Little made a strong start in the House, in his first week telling Mr Key to "cut the crap" over the "smear campaigns" he said had been run from the PM's office involving former adviser Jason Ede and Mr Slater.
But he has not exactly made a grand entrance in his debut in the preferred prime minister stakes, rating as the first choice of 13.6 per cent of those polled.
Mr Key is preferred by 65 per cent, a slight rise of 0.7.
But almost 50 per cent reacted positively when asked how they rated Mr Little's performance - 24.7 per cent said "good", 19.4 per cent "very good" and 5.3 per cent "excellent". Another 23 per cent said it was "adequate" and 7 per cent "poor".
Questioned on party affiliation, 24.2 per cent of those polled said they voted Labour last time and were likely to again.
But more encouraging for Labour is that 14.3 per cent said they had not voted Labour last time but were likely to do so next time.
Mr Little's early polling figures are less pronounced than were his predecessor's. Mr Cunliffe began with 16.8 per cent personal support soon after his election as leader in September last year, and Labour peaked at 37.7 per cent before a gradual decline to 25.13 on election day a year later.
But Mr Cunliffe was once a minister and had a higher profile and the leadership contest, prompted by David Shearer's resignation, was a high-profile event.
All three previous Labour leaders, Mr Cunliffe, Mr Shearer and Phil Goff, got the party to a peak of just above 35 per cent in the polls and peaked in personal support at 18 per cent or 19 per cent.
Mr Little's election was announced on November 18. He narrowly beat Grant Robertson, who won more support from the caucus and the party membership.
But Mr Robertson's public profile remains low. He is preferred prime minister by only 0.6 of respondents, behind Mr Cunliffe on 2.8, former Prime Minister Helen Clark on 2.3 and MP Jacinda Ardern on 1.7 per cent.
New Zealand First is down 2.8 points in the poll to 5.6 per cent and the Greens are down 1.6 to 9.5 per cent. They polled 8.66 per cent and 10.7 per cent respectively in the election and have been overshadowed since by the formation of the government and the Labour Party's leadership ructions.
Mana, which did not get back to Parliament, polled 0.2 per cent, higher than United Future, which got back in. Internet Mana polled 1.42 per cent at the election, which would have brought in two MPs if Mana leader Hone Harawira had not lost his seat.
The Maori Party is up a little to 1.5 per cent.
