Based on the concept of chattering controls originally given by Gamkrelidze, a new algorithm is proposed for nonlinear optimal control problems with non-convex constraints on control, where the value of the control is restricted to just a compact set, not necessarily to a compact ’convex’ set. These problems include an optimal control problem using quantized controls, which is one of the major problems from a practical point of view. Accumulation points generated by the proposed algorithm, if they exist, are shown to satisfy the maximum principle (necessary conditions for optimality). The implementability of the algorithm is also shown by simulation experiments.