Mr Brownlee wouldn't comment because the matter is before the courts.
At issue is the Government's offer of 50 per cent of the value of their land.
The claimants want the same compensation offer other red zone properties owners received - the 2007 rateable value of their properties.
Bare land cannot be insured, which left many people facing huge financial burdens when the magnitude-6.3 February 22, 2011 quake struck.
They are bringing the action against Mr Brownlee and Roger Sutton, chief executive of the Canterbury Earthquake Recovery Authority.
"These property owners have suffered tremendously because of unlawful decisions by the minister and the chief executive,'' said group spokesman Ernest Tsao.
"We think the evidence will show that the Crown acted with complete disregard for New Zealander's property rights and human rights.''
Quake Outcasts is confident its case will establish that Mr Brownlee's decision to establish red zones was unlawful and "obliterated'' the market value of their properties.
They also think his decision as to who was deserving of compensation, was unlawful and not for any proper purpose.
Mr Brownlee's decision sought to ``avoid statutory processes and to unlawfully drive down costs regardless of who it hurt in the process'', the group claims.
Quake Outcasts believes the case has widespread implications for New Zealanders' property rights.
A date for the hearing, expected to last 2-3 days, will now be set down, probably within three months.