Abstract In this paper, we consider second order elliptic problems with rapidly oscillating coefficients. On basis of [O.A. Oleinik, A.S. Shamaev, G.A. Yosifian, Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdam, 1992; Wen-ming He, Jun-zhi Cui, A pointwise estimate on the 1-order approximation of G x 0 ε , IMA J. Appl. Math. 70 (2005) 241–269] we propose a new approximate method to solve these problems. Of course, we present its error estimate.