In this paper we apply an approximate method based on Galerkin approach with Legendre wavelets basis, on a class of fourth order boundary value problems. The approach reduces the main equation to a system of linear algebraic equations that could be solved numerically. The operational matrix of the method is obtained, and the convergence of the method is proved. we approximate the solution and its higher order derivatives, for some special examples and compare the results with some other numerical methods. The results show the effectiveness of the proposed method.