Let \(L_\varepsilon\) be a family of operators indexed by a small parameter \(\varepsilon\) and let \(u_\varepsilon\) solve the equation \(L_\varepsilon u_\varepsilon= f\). If \(u_\varepsilon\to\overline u\), the homogenization problem can be roughly stated as to find an operator \(\overline L\) such that \(\overline L\overline u= f\). Following some works of M. E. Bewster and G. Beylkin [Appl. Comput. Harmon. Anal. 2, No. 4, 327-349 (1995; Zbl 0840.65047)] in which they use a multiresolution analysis (MRA) to the homogenization of an integral equation, the author describe homogenization for one-dimensional elliptic equations in divergence form using wavelets spaces. In this framework, homogenization is reduced to projecting the solution of the original equation from the fine resolution space of the MRA onto the coarse one. The results are proved in the simplest multiresolution analysis, the Haar system. Boundary conditions of periodic, Neumann and Dirichlet types are considered. Some numerical experiments are presented.