The policeman came off night shift on Sunday morning and went to visit his parents in Bilbao's Barakaldo neighbourhood.
He then allegedly shot his 79-year-old father and 80-year-old mother before taking his own life, local newspaper Diario Vasco reported.
The bodies of the three were found late afternoon on Sunday with obvious signs of violence, but it is not known what time the three died.
Police investigating the case said they did not believe anyone else was involved.
Barakaldo mayor Alfonso García said the incident was "sad and explicable", describing the officer involved as "very professional" and a "good neighbour".
Regional daily La Voz de Galicia reported work colleagues as saying that the agent had been acting strangely on Saturday night during his final shift.
The paper also reported the illness of the man's parents, but the causes for the tragedy are yet to be established.