A plunger oil-well pump and its plunger are provided. The plunger comprises a plunger core (2) whose outer wall has some liquid passing holes (4). A flexible sealing sleeve (3) is set around the outer wall of the plunger core. The flexible sealing sleeve (3) is such located that it can cover said some liquid passing holes (4) in the plunger core (2). The plunger solves the problem of bad coaxiality, ellipticity and severely biased friction between the sealing means of the hydraulic plunger pump and the pump cylinder. The requirements for machining accuracy and mounting of the plunger are low. The plunger has better sealing performance.
