Officers were initially called around 4 p.m. to a residence in the 500 block of N. Fifth Street.
When they arrived, officers learned the suspect had fled the scene to a wooded area adjacent to Alvin Missionary Baptist Church.
According to Alvin police, officers gave repeated commands for the man to drop his weapon. After placing the weapon on the ground, police say, he brought it back up as officers moved in on him.
One officer fired at the suspect, investigators said.
The suspect was taken to a local hospital where he was pronounced dead.