We say that a matrix X∈Rm×n is real (R, S) symmetric matrix if X=RXS, where R∈Rm×m and S∈Rn×n are real nontrivial involutions; thus R=R-1≠±Im, S=S-1≠±In. In this paper we apply the augmented Lagrangian method, for minimizing general smooth functions on convex sets in optimization theory, to solve the (R, S) symmetric matrix least squares problem under a linear inequality constraint. That is, given positive integers m, n, p, t, q, matrices Ai∈Rm×m, Bi∈Rn×n (i=1,2,…,q), C∈Rm×n, E∈Rp×m, F∈Rn×t and D∈Rp×t, find a (R, S) symmetric matrix X∈Rm×n that minimize||AiXBi-C||under matrix inequality constraint EXF ≥ D, where EXF-D means that matrix EXF -D nonnegative. We present matrix-form iterative format basing on the augmented Lagrangian method to solve the proposed problem and give some numerical examples to show that the iterative method is feasible and effective.