The robberies have happened between the 9600 to 11000 block of Westheimer.
Police said the suspect commits the crime the same way every time.
In early November, HPD reported the man approached an employee at a drugstore and told her he wouldn't harm her if she did not call the police.
The man then placed several cartons of Newport cigarettes into a trash bag and ran away.
HPD said they believe the same suspect is responsible for three other robberies at convenience stores in the same area between Nov. 2 to Nov. 13.
Police described him as a Black male, between 30 to 35 years of age, weighing anywhere from 130 to 160 pounds and standing 5'5 to 5'7 in height.
Any information related to these robberies can be reported by calling Crime Stoppers at 713-222-8477.