In an interview with police, Mr Walker said he believed at the time that Ms Taylor's ex-boyfriend, Jamarcus Glover, had broken in, according to the New York Times.
Ms Taylor's family sued Louisville authorities in May and reached a $12m (£9.4m) settlement.
What does the latest lawsuit say?
In a statement, Mr Mattingly's lawyer alleged that his gunshot wound nearly killed him, and as a result he was "entitled to, and should, use the legal process to seek a remedy for the injury that Walker has caused".
Mr Walker was initially arrested and charged with attempted murder, but the suit was later dropped. He is currently suing Louisville police and seeking immunity from prosecution under Kentucky's "Stand Your Ground" law.
The controversial legislation grants people the right to defend themselves, with lethal force if necessary, if they believe they are under the threat of bodily harm or death.
"If Kenny can be sued for defending himself, make no mistake, all lawful gun owners' rights are at risk. And that should scare everyone," his lawyer told the Louisville Courier Journal newspaper.
Why did officers storm the home?
On the night of the raid, police were executing a search warrant as part of a drugs investigation.
The warrant obtained by police included Ms Taylor's name and address. Authorities believed Mr Glover was involved in a drug ring and had used her apartment to hide narcotics.
No drugs were found at the property, though Jefferson County Prosecutor Thomas Wine said the search was cancelled after the shooting.
Mr Glover was arrested for drug possession on the night of Breonna Taylor's death.
He has said that prosecutors pressed him to name Ms Taylor as a "co-defendant" in the case against him.