A numerical method based on finite difference scheme with uniform mesh is presented for solving self-adjoint singularly perturbed two-point boundary value problems. First, the original problem is reduced to its conventional form and then, the reduced problem is solved by using sixth order stable central difference method. To demonstrate the applicability of the method, numerical illustrations have been given. Graphs are also depicted in support of the numerical results. The stability and convergence properties of the method have been examined. The method approximates the exact solution very well and gives more accurate solutions than some methods found in the literature.