Article:David Crompton will challenge the decision to ask him to resign after the inquests which found the 96 Liverpool fans were unlawfully killed.
Five Hillsborough relatives asked to make submissions at the High Court but were refused and landed with his costs.
Their lawyer Elkan Abrahamson said the families were "upset".
More than £4,500 has already been donated to the appeal and the families have vowed to give any extra money raised to Alder Hey Children's Hospital in Liverpool.
Mr Abrahamson said: "It's great people are prepared to help the families.
"David Crompton is perfectly entitled for his costs to be paid, it's just unfortunate that that causes distress to the families so we're committed to ensuring that they personally don't have to pay from their own pockets.
"Most of them can't anyway."
Mr Crompton was asked to resign from his position as chief constable of South Yorkshire by Police and Crime Commissioner Dr Alan Billings following the verdict of the Hillsborough inquests into the disaster on April 15 1989.
He was suspended over fears about public trust in the force.
Mr Crompton was criticised by the families over the stance taken by police lawyers during the inquest, which concluded police conduct contributed to or caused the disaster.
Following the ruling, Mr Crompton reiterated an apology for the tragedy and said he accepted the findings of the inquest.
The judicial review will be heard at the High Court in London on March 28 and 29.

A summary of the above article is?
A crowdfunding site has been set up to help Hillsborough families pay the £28,000 legal costs of a former South Yorkshire Police chief constable.