The lawsuit was filed Wednesday by the victim's daughter, Ashley Sanchez.
The collision happened the afternoon of March 18.
Klinghoffer was driving a black SUV when he failed to see 47-year-old Israel Sanchez crossing the street and struck him, the lawsuit said. Sanchez later died.
The lawsuit also alleges Klinghoffer was using a cellphone while driving, as video footage shows the driver holding an object above the steering wheel. Video also shows a 40-foot-wide grassy median dividing the road that should have given Klinghoffer time to see pedestrians in the crosswalk, the lawsuit said.
Israel Sanchez was on his way to the grocery store to buy food to cook for his daughter and her two sons when he was hit.
Klinghoffer has not been charged with any wrongdoing.
"I haven't recovered," said Ashley Sanchez. "It's a daily basis that I break down, and it's hard when you're a single mom, trying to be ok and show them you're fine, but in reality, it's eating you alive. I want him to be held accountable. I want there to be awareness. It's not the first incident that's happened in that intersection."
She described her father as a great chef and a great artist, saying he was "very loving and joyful."
"I have one of his paintings here that he painted me a few years ago when I was at school," she told ABC7 on Wednesday. "He would take me as a little baby and make me spaghetti. I have all those memories, memories he was able to do with his grandkids."
Klinghoffer is currently on tour with the band Pearl Jam with a show in Madrid scheduled for Thursday, July 11.
"The police officers don't check his phone to see if he was on the phone, and they just take his word for it," said Nick Rowley, the attorney for Ashley Sanchez. "Could it possibly be because he's the guitarist for Pearl Jam, because he played for the Red Hot Chili Peppers for 10 years? I'm really disappointed in law enforcement here. They didn't do their job here. This man should have been arrested. They should have checked his cell phone. We have the video evidence to show he was playing with a device, driving distracted. He's been charged with nothing. He wasn't even given a citation."
A statement from Klinghoffer's lawyer said, "This was a tragic accident. After which, Josh immediately pulled over, stopped the vehicle, called 911, and waited until police and the ambulance arrived. He is fully cooperating with the traffic investigation."
Rowley hopes police will reopen their investigation after seeing the surveillance video.
The Associated Press contributed to this report.