A hydraulic pressure control apparatus for a torque converter includes a relay valve switching levels of a hydraulic pressure in the hydraulic power transmission chamber and establishing selective connections between a cooler and the hydraulic power transmission chamber or between the cooler and a hydraulic pressure supply source of which a flow amount of the operational fluid is regulated by a first orifice, an electronic control unit controlling operations of the relay valve, a hydraulic pressure declination determining portion judging whether the hydraulic pressure of the hydraulic pressure supply source is lower than a threshold value based on a predetermined vehicle state, and a switching command outputting portion outputting a command to connect the cooler and the hydraulic pressure supply source by the relay valve when the hydraulic pressure declination determining portion determines that the hydraulic pressure of the hydraulic pressure supply source is lower than the threshold value.