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We study the acceleration of electrons in a system of linearly polarized laser wave, propagating at small angles to the direction of electron motion. The parameters of electron bunch and laser wave are chosen so, that during driving electrons in a band of a wave, the electric field of a wave has not changed the direction. The requirements of deriving of maximum rate of acceleration are found depending on parameters of electronic bunch and laser wave. It is shown, that the dependence of growth of electrons energy from number of light bands has nonlinear character. The influence of light diffraction on process of acceleration is considered. It is shown, that the discussed scheme of acceleration allows a possibility of deriving of high acceleration rate owing to existence of modern powerful lasers.
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