Walter Hinton, 38, is accused of shooting and killing 60-year-old Robert Jones.
The shooting happened around 1:10am Saturday during a birthday party at a small apartment complex in the 3000 block of Truxillo near Ennis.
According to the Houston Police Department, Hinton was at the birthday party when Jones' dog allegedly bit him on the leg.
Hinton got into an argument with Jones and left the party, but police said he returned with a gun and started shooting.
Jones was struck in the abdomen and died at the scene.
Hinton's bullets also hit two other men. They were rushed to Ben Taub General Hospital where one was treated and released and the other underwent surgery. Both of the injured men are expected to recover.
Hinton fled the scene in an unknown direction, driving a white 2000 Chevrolet Impala with Texas licence plate number BL2-B827. He has not been seen since.
Anyone with information in this incident or on the whereabouts of Hinton is urged to contact HPD Homicide Division at 713-308-3600 or Crime Stoppers at 713-222-TIPS. All Crime Stoppers tipsters remain anonymous and could be eligible for a reward.