A theoretical analysis of a least-squares mixed finite element method for second-order elliptic problems having non-symmetric matrix of coefficients is presented. It is proved that the method is not subject to the Ladyzhenskaya-Babuska-Brezzi (LBB) condition and that the finite element approximation yields a symmetric positive definite linear system with condition number O(h(-2)). Optimal error estimates are developed. (C) 2000 Elsevier Science Inc. All rights reserved.