The incident took place last night and the accused, Digambar, also shot at his step-mother but her condition is stable. He has been arrested, they added.
The pistol used in the crime has also been seized.
The accused was posted in the Central Reserve Police Force as a constable but left his job around three years back.
His father, Narsingh, 55, was a property dealer.
After Digambar left his job, he was doing small time jobs for the property dealers, a senior police officer said.
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Last night, the father-son duo had a quarrel on the land issue. Digambar went into his room, took out his pistol and shot his father twice at his chest.
When his step-mother tried to intervene, he fired at her and the bullet hit her hand.
The police were informed about the incident by locals after the gunshots rang out. They rushed the injured couple to hospital.
Narsingh was declared brought dead while his wife was undergoing treatment, he said.