A student from Hamilton is getting her day in court today as she takes on the Government over its climate change policies.

Sarah Thomson's High Court hearing, where she's alleging the government is not doing enough to tackle climate change, is underway in Wellington - it's the first case of its kind.

The 26-year-old law student is challenging the government policy on cutting greenhouse gas emissions, accusing it of failing to review emissions targets properly and using flawed economic modelling in its policy decisions.

The Government's carbon emission reduction goals set in 2011 promises a 50 percent reduction in greenhouse gas emissions by 2050.

Ms Thompson’s lawyer, Davey Salmon, said there's been a lot more research since that target was set, and it doesn't even match up to our promises at the global Paris accord.

"We have a curious world in which the Minister has decided not to exercise the statutory power to review the 2050 goal even though it doesn't conform or sit with the NDC goal which relates to 2030."

Climate change minister Paula Bennett said the government is standing by its actions and is comfortable with its Paris Accord target.

Bennett said the target was set after a thorough process of consultation.

Supporters have loudly rallied outside the court with banners and instruments.

Michelle Ducat from Oil Free Wellington said they wanted to show solidarity.

"It's a groundbreaking case. She is showing and helping provide that forum where we can all come together and say we need to work together urgently."