It happened just before 6 p.m. Wednesday at Gellhorn and the East Freeway.
Undercover deputies with a sheriff's office task force spotted the vehicle Wednesday morning and started following it, along with DPS troopers.
The black Mazda was taken in an aggravated robbery in Humble sometime earlier, investigators said.
The officers finally decided to stop the car by using unmarked vehicles to pin it in.
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Officials said a DPS trooper walked to the driver's door of the car, trying to get the suspect out when the suspect put the car in reverse ramming officers' vehicles.
"He began to violently back up and as a result of him violently backing up and almost hitting officers, they discharged their weapons," Houston Police assistant chief Sheryl Victorian said.
At least two troopers and a deputy fired at the suspect. Deputies and troopers performed CPR, but he was pronounced dead.
Amazingly, a woman in the vehicle with him was not hurt.
"She is now a witness. We don't believe she was involved in the aggravated carjacking," Victorian said.
No law enforcement officers or bystanders were hurt. Officials couldn't say whether the suspect was armed.
"We haven't conducted a complete search of the vehicle at this time. He was using the vehicle as a weapon to strike other vehicles at the time of the incident," regional director of DPS Jason Taylor said.
Sheriff Ed Gonzalez said the suspect, whose name hasn't been released, is thought to be connected to at least two other robberies and may be linked to more.
"At least two more aggravated robberies. Not auto thefts, aggravated robbery that have occurred over the span of at least two days. So there may have been some type of crime spree going on," he said.