Abstract: In a clutch pressure control apparatus wherein clutch engagement pressure is automatically controlled according to engine speed based on a first function, engagement shock may occur due to an excessive clutch pressure in a case where the acceleration pedal is depressed with the transmission being placed in a NEUTRAL position and being shifted to a running position. To solve this problem, the apparatus comprises a controller including a second function. When an actual engine speed at the initial clutch engagement exceeds an allowable engine speed, clutch pressure is first set to a temporary low value not exceeding the allowable engine speed, and then while incorporating the second function, is allowed to approach that value to be determined according to actual engine speed by the first function.