The Climate Change Commission declined to comment on the action.
"We have received a copy of the proceedings from Lawyers for Climate Action today, and we will be taking the time to review them," chairman Dr Rod Carr said in a statement.
"As this is a matter that will be before the Court, the Commission has no further statement to make at this time."
In June, the commission submitted its final advice to the Government, warning New Zealand was not on target to meet its obligations to the Paris climate agreement (which aimed to limit global warming to 1.5C) and laid out what might be required to do so.
The report spelled out the need to reduce herd sizes, import fewer petroleum vehicles and plant trees to get the country on a path to meet 2050 climate goals.
But the challenge from LCANZI claims the report contains "a logical and mathematical error" because it applied carbon reduction targets from 2010 levels (the starting point for the Paris targets) to New Zealand's gross emissions, rather than its net emissions.
Whereas the commission calculated that New Zealand's net emissions from 2021-2030 should be no more than 568 metric tonnes (Mt) of carbon dioxide equivalent, LCANZI says using its methodology the limit would be a net emissions limit of 484Mt.
According to LCANZI the alleged error has already been pointed out to the commission after the submission of its draft advice. A statement released on Friday says Statistics New Zealand uses the methodology it suggests.
Jenny Cooper QC and James Every-Palmer QC wrote to Shaw on June 17 pointing to "what we believe to be an important error" in the analysis.
"The Climate Change Commission's advice looks ambitious on a first glance. However, when you dig into the detail, it fails to adequately address the scale and urgency of the task and is inconsistent with the legislation and international agreements it is meant to address," Cooper, the society's president, said in a statement.
"The Commission set a target for 2030 net carbon dioxide emissions by applying the specified percentage reductions to our 2010 gross carbon dioxide emissions. The result implies that our net carbon dioxide emissions can increase between 2010 and 2030 which is nonsensical."
Every-Palmer said the purpose of the judicial review "is to ensure that the commission has clear guidance on what is required".
This morning Cooper said she hoped the society would be granted a hearing before the end of the year.
Matt Burgess, an economist at the New Zealand Initiative, which has also been ciritical of the commission's report - for different reasons - said the society's "look right".
Ah added: "I would say the Commission has a serious problem on its hands."
