Within the framework of Eikonal multiple-scattering theory, the Coulomb effect in π^±-⁴⁰Ca elastic scattering is studied. The calculating program for the differential cross section is worked out by FORTRAN 77 and the results are in good keeping with the experimental data, indicating that the Coulomb effect does not only enhance the small angle differential cross section, but also fill up the dips of differential cross section.