A press-forming apparatus includes a punch, a die having an inclined surface, and a die holding plate. A blank holder has a holding surface, and a die load sensor detects a load in a pressing direction, a load in a first direction perpendicular to the pressing direction, and a load in a second direction perpendicular to the first direction. A controller calculates a normal force of the die based on the loads in the pressing direction, in the first direction, and in the second direction. The loads are detected by the die load sensor, and the controller calculates the amount of correction of clearance between the die and the blank holder based on the normal force of the die. The first driver moves the die in the pressing direction based on the amount of correction of clearance, and a second driver drives the punch in the pressing direction.