An apparatus and a method of controlling a water supply of a washing machine, which naturally discharges the water within a detergent dissolving unit when the water level within the detergent dissolving unit is more than a designated water level so as to prevent the water within the detergent dissolving unit from overflowing, and warns of a clogging error in a water supply path when a number of times the water level within the detergent dissolving unit is more than a designated water level, is more than a designated number of times. Whether or not the water supply is provided is determined according to the number of times the water level within the detergent dissolving unit is more than the designated water level sensed by the water level sensor, thereby controlling a water supply action so as to stop the water supply only under abnormal conditions from supplying the water to a water tank, and improving a reliability of the apparatus.