It happened shortly after nine o'clock Friday night on Bettis Avenue.
Officers were sent to the scene after gunshots were reported in the area of 217 and 219 Bettis.
Clifford Daniel Stafford, 31, of West Memphis, died after being taken to Crittenden Regional Hospital for treatment of his injuries.
The other man who was shot was treated and released from a Memphis hospital.
West Memphis Police detectives worked the crime scene and conducted interviews well into the night and early morning, They are following up on leads, but have made no arrests.
The West Memphis Police Department is asking anyone with information on this incident to call Crittenden County Crime Stoppers at (870) 732-4444.
Crime Stoppers will pay a reward of up to $2,000 for information that leads to an arrest in this case.