It happened at 11:00 Saturday morning along the 2000 block of East Firth Street in Kensington.
The suspect, identified by police as 22-year-old Minnie Collins, was sitting on the front steps.
Police say the victim pulled up in a black SUV with her two children - an infant and a teenager.
The victim got out to tell the suspect to get off her mother's front steps.
That's when Collins allegedly jumped in the vehicle and sped off - that is until Frank Shipley forced her to stop at Cumberland and Frankford.
The father of his own four says his paternal instincts kicked in when he heard those piercing screams.
"Basically I was in my house with my wife and my daughter, about to go to work. I heard this lady outside screaming that someone had took her car and her kids. I heard the car speed off so I ran and got in my car and chased them down," said Shipley.
He held the suspect down, waiting for police to arrive.
"I opened the door and once I opened the door I saw the person wasn't paying attention. Right away I grabbed the person," said Shipley.
Kenny Phy shot cell phone video of the incident. He ran to the scene.
He says the mother of the children was frantic.
"She was a mess, basically in distress, trying to keep it together, saying 'My baby!' She couldn't keep it together," said Phy.
"The baby was awake in there. All wide eyed, thank God. That lady had no respect for that baby at all," said Shipley.
Why Collins allegedly stole the vehicle is unclear. It is not known if she knew the children were inside.
She faces a list of charges including Kidnapping, Carjacking, Robbery, Reckless Endangerment and others.
Meanwhile, Shipley is being called a hero.
"I don't know about hero but it feels good to help out and make sure everyone is safe," he said.