The grip position calculator determines a grip position where the fingers can grip a workpiece in any orientation of the workpiece. The calculator then determines an initial position where the finger tips can grip the workpiece and set the initial position as a point of calculation. Then an allowable gripping force is calculated which is an index that indicates an allowable force to be applied to the workpiece at point. Then other allowable forces are calculated for a plurality of points near the point of calculation. Then the point of calculation is selected as a possible gripping position if the allowable force a point is greater than any of the allowable forces. Otherwise, one of the points is selected for another point of calculation where the greatest allowable force (De) has been calculated and return to calculating an allowable gripping force.