We consider an optimal control problem in which the state equation has rapidly oscillating coefficients (characterized by matrix A epsilon, where epsilon is a small parameter). Based on some important results from the paper by S. Kesavan, we convert this optimal control problem to a partial differential equation problem. Therefore, solving optimal control problem is equivalent to solving this partial differential equation problem. By several numerical examples in one dimensional case, we also show that the limit satisfies a problem of the same type but with matrix A 0 (the H-limit of Aepsi).