A comprehensive (start-to-end) simulation was performed regarding the formation of a front-tilted laser pulse and the subsequent acceleration of non-relativistic electrons moving along a reflective grating structure. The laser pulse tilt was formed using another diffraction grating – either reflective or transmissive. The pulse had a spectral range (FWHM) of 803–863 nm and an initial duration of approximately 17 fs. Acceleration under normal laser pulse incidence was also calculated for comparison. Research results indicate that the use of a femtosecond laser pulse with a front, tilted by means of a reflective diffraction grating, significantly enhances the efficiency of laser acceleration of non-relativistic electrons compared to the case of a pulse at normal incidence. Furthermore, it was found that using a transmissive diffraction grating to shape the tilted pulse front also increases acceleration efficiency relative to normal incidence on the accelerating grating, although the acceleration rate is lower than when a reflective diffraction grating is used.