The effect of two intense cross-focused cosh-Gaussian laser (CGL) beams on the generation of electron plasma wave (EPW) and particle acceleration in collisionless plasma has been investigated under the relativistic–ponderomotive regime. Due to mutual interaction of two laser beams, cross-focusing takes place in plasma. The EPW is generated by the beating of two cross-focused CGL beams of frequencies ω1 and ω2. An analytical expression for the beamwidth of laser beams and EPW as well as the power of the generated EPW has been evaluated using Wentzel–Kramers–Brillouin and paraxial approximations. The energy of the accelerated electrons by the beat-wave process has also been calculated. Numerical simulations have been carried out to investigate the effect of typical laser plasma parameters on the power of excited EPW and acceleration of electrons. The results are compared with only relativistic nonlinearity and the Gaussian profile of laser beams. It is observed that CGL beams focused earlier than Gaussian beams, which significantly affected the dynamics of plasma wave excitation and particle acceleration. Numerical results indicate that there is a remarkable change in the power of generated EPW and electron acceleration in the relativistic–ponderomotive case in comparison with only relativistic case.