A draining pump for a washing machine and the washing machine thereof are disclosed. The washing machine includes an inlet system, and a draining system containing the draining pump device. The draining pump has a draining motor, a pump shell, a spinning blade and a filter, wherein, an inlet nozzle and an outlet nozzle are also arranged on the pump shell, and the pump shell is internally arranged with a front pump chamber and a rear pump chamber which are communicated according to the water draining sequence; the spinning blade is arranged in the rear pump chamber and installed coaxially with a revolving shaft of the drain motor, the filter is arranged in the front pump chamber, and a pressure relief plate with pressure relief holes is arranged at one side of the outlet of the filter corresponding to the water spinning blade.