We consider a control volume (covolume) method for second-order elliptic PDEs with the rotated-Q(1) nonconforming finite element on rectangular grids. The coefficient K may a variable, diagonal tensor, or discontinuous. We prove first-order convergence in H-1 norm and second order convergence in L-2 norm when the partition is square. Our numerical experiments show that our covolume scheme has about 30% less error than FEM even when K is discontinuous tensor. (C) 2007 Elsevier Inc. All rights reserved.