This paper presents and analyzes the focusing of pump beams and the excited EPW (electron plasma wave) in a PBWA (plasma-beat-wave accelerator) by beating two self-trapped laser beams. The equations governing the saturated amplitudes of EPW in nonuniform pump beams have been derived analytically. With these, the condition for self-trapping of pump beams has been studied self-consistently. The optimum frequency mismatch parameter and the corresponding optimum initial plasma density as well as the maximum amplitde of the EPW have been obtained analytically. The transverse distribution of the EPW for Gaussian pump profiles has been calculated numerically and shows peculiar characteristics for certain frequency mismatch parameters. In addition, the component of the EPW electric field due to the nonuninformity of pump beams has been obtained and its influence on particle acceleration in PBWA has been briefly discussed.