In the present study, the shape optimization of a golf club is investigated. The optimization of thickness distribution of a clubface is studied for maximizing the release velocity of the ball under the constraint of a constant amount of the clubhead weight The basis vector method, which is an approximate method for the optimization problems, is employed because the sensitivity cannot be derived analytically. The basis vector represents the fundamental change of the shape, and it is preferable for obtaining effective results that the basis vectors are independent mutually. The eigenmodes is used to create the basis vectors in a 3-dimensional problem. The theory of impedance matching is comfirmed numerically by a 2-dimensional example. A 3-dimensional example is given to show that this approach is effective to optimal design of golf clubhead.