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The man was found by the property manager and a security guard. He was unresponsive and suffering from an apparent gunshot wound.
The property manager told police that a resident notified them that front door to the unit where the man was found was open all night.
Paramedics responded to the scene and pronounced the man dead.
His identity has not been released.
Police have no known suspects at this time and are unaware of a motive.
Anyone with information in this case is urged to contact the Houston Police Department Homicide Division at 713-308-3600 or Crime Stoppers at 713-222-TIPS.