Wavelets, which have many good properties such as time/frequency localization and compact support, are considered for solving the Hamilton-Jacobi-Bellman (HJB) equation as appears in optimal control problems. Specifically, we propose a successive wavelet collocation algorithm that uses interpolating wavelets in a collocation scheme to iteratively solve the generalized-Hamilton-Jacobi-Bellman (GHJB) equation and the corresponding optimal control law. Numerical examples illustrate the proposed approach.