We consider an optimal control problem in which both the state equation and the cost functional have rapidly oscillating coefficients (characterized respectively by matrices A(epsilon) and B-epsilon, where epsilon is a small parameter). We make no periodicity assumption. We study the limit of the problem when epsilon --> 0 and work in the framework of H-convergence. We prove that the limit satisfies a problem similar to the original one but with matrices A(0) (the H-limit of A(epsilon)) and B-# (which is a perturbation of the H-limit B-0 of B-epsilon). We also study some particular cases. This paper extends former results obtained by Kesavan and Vanninathan in the periodic case.