The latest suspect, who has not yet been identified, was taken into custody after fleeing from investigators, according to Galveston County Sheriff Henry Trochessett.
Investigators are now searching the man's residence on Westwood.
On Wednesday, two other men were arrested.
The Galveston County Sheriff's Office was able to track 23-year-old Jamie Posada and 21-year-old Ricardo Posada to Houston where they were taken into custody.
It's not clear if the men are related.
The men told police they were asked by a third man to go to the location to commit a burglary but that it was not planned to hurt anyone.
The killing happened on FM 517 near Algoa-Friendswood. Authorities say the victim, who was shot several times, was an employee of Bradshaw nursery, where he was found.
The victim's identity has not been released.
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