3-D optimization method using the finite element method and the Rosenbrock's method, is developed to apply to the optimal design of permanent magnet type of retarder. The Rosenbrock's method has an advantage that the optimal value can be obtained within small number of iterations compared with the stochastic methods, such as simulated annealing method. As the number of searching iterations of the Rosenbrock's method is affected by the initial condition and the constraints, the experimental design method is introduced to the determination of appropriate values of them. A technique for modifying the hexahedral mesh is conceived in order to change the shape of machine at each iteration for the optimization. The obtained result is discussed from the viewpoint of flux and eddy current distributions. It is shown that the number of iterations and CPU time can be reduced by using the experimental design method. The braking torque is increased about 50% by using the optimization method.