On Tuesday, the Galveston Police Department said a task force team arrested Larry Ballard during a traffic stop in the 2400 block of Broadway.
Over the weekend, police said officers responded to Avenue N 1/2 , near 17th Street, just before 7 p.m. Saturday.
Officers said they found 29-year-old David Rodriguez inside a vehicle with gunshot wounds.
An investigation led authorities to Ballard, who is currently being held in the Galveston County Jail on a $500,000 bond.
It's unclear how both men knew each other.