There is provided a hydraulic pressure control apparatus for a vehicular hydraulic power transmission device with a lock-up clutch, in which an increase in the temperature of hydraulic oil in an engagement side oil chamber is suppressed, durability of frictional material is improved, and the lock-up clutch is appropriately controlled. A switching control valve (a lock-up relay valve 250 and a lock-up control valve 252) switches between connection and disconnection between each of two oil passages that communicate with an engagement side oil chamber 31, and each of a high pressure oil passage and a low pressure oil passage, according to the operating state of the lock-up clutch 11. For example, when the lock-up clutch is completely engaged, the hydraulic oil is supplied to both the two oilpassages from the high pressure oil passage, hydraulic pressure PON in the engagement side oil chamber 31 is increased, and a sufficient transmission torque capacity of the lock-up clutch 11 is obtained. When the lock-up clutch 11 is in the slip state, one of the two oil passages is connected to the high pressure oil passage, and the other oil passage is connected to the low pressure oil passage such that the hydraulic oil is circulated in the engagement side oil chamber 31. Therefore, an increase in the temperature of the hydraulic oil is suppressed, the lock-up clutch 11 is cooled, and the durability of the frictional material 36 is improved.