A spectral method based on the Legendre polynomials for solving Helmholz equations was proposed. Withan explicit formula for the Legendre polynomials in terms of arbitrary order of their derivatives, the successive integrationof the Legendre polynomials was represented by the Legendre polynomials. Then the method was formulized for second-order differential equations in one dimension and two dimensions. Numerical results indicate that the suggested method issignificantly accurate and in satisfactory agreement with the exact solution.