The show, Forensics NZ, is a multi-episode prime time documentary series.
Each episode focuses on a single crime from the past decade that was solved by the combination of crime investigation and forensic science.
The cases cover blood spatter, DNA, tool marking, digital forensics, toxicology, entomology, and the latest in cutting-edge scientific technology.
Reid took exception to his case being included in the second season of Forensics NZ.
Earlier this month the High Court at Auckland heard that Reid intends to reopen his case and seek a further appeal or retrial.
He argued that the show could present a "real risk of prejudging matters or issues that are to be imminently before the courts especially in the event that [his] appeals are allowed in whole or part thereby resulting in a retrial".
Reid was convicted and sentenced for the rapes and murder in 2008.
In 2009 an appeal against his conviction was dismissed in the Court of Appeal.
In 2012, the Supreme Court dismissed Reid's application to appeal further.
The only realistic option Reid has left in terms of appealing his conviction and sentence would be to apply for a Royal Prerogative of Mercy.
There has been no application for such proceedings.
SPP lawyer Simon Mount told the court that Reid had "exhausted all criminal appeal rights".
He said for that reason, the airing of Reid's case on Forensics NZ would not affect his case.
"For that reason, [Reid] falls well short of establishing an arguable claim that the case is sub-judice, or any other basis for relief."
Justice Kit Toogood reserved his decision until today.
He said Reid had a "fundamental flaw" in his application.
"There is no appeal and there is no proceeding in which contempt of Court or any application of a sub-judice risk can be considered," he said.
"[Reid's] case has no prospect of success and I order that [the injunction application] be struck out."
Justice Toogood said SPP was entitled to costs - although acknowledged that seeking costs from Reid "may be futile".
This was not the first time Reid has taken action to try to prevent television shows airing information about his case.
In December 2016 he went to the High Court to try to stop TVNZ broadcasting a show about him.
Radio New Zealand reported Reid told the court that a programme they featured on their website and which could be viewed by its audience on demand, contained inaccuracies that could affect his right to a fair trial.
He maintains he never raped or killed Agnew and that he has been wrongly convicted.
He also hit the headlines last year when he married disgraced lawyer Davina Murray in prison.
Murray, who now uses Reid's surname, represented her now-husband for a time, but lost her legal career after smuggling an iPhone, cigarettes and a lighter to him in 2011 in Mt Eden prison.
