For the eigenvalue problem of real symmetric interval matrixes, the uncertainties of the interval are thought as one perturbed quantity around the midpoint of the interval. In this paper an Evolution Strategy Algorithm is presented for solving the eigenvalue problem of interval matrixes based on the expansion of the interval. Taking the center point of the interval matrix as the balancing point and the interval indefinite quantity as the perturbation quantity, the solving the minimum and maximum eigenvalues of the interval matrix by perturbation formulas, the solution of the eigenvalue problem is obtained. The example which is given in the article has illustrated that the algorithm is effective. The main feature of the algorithm is that the result region is very accurate and the convergence speed is fast.