The laser acceleration of electrons in a helical ondulator with a medium is considered, providing there is no Cherenkov interaction. An expression for the rate of acceleration is obtained by the method of the theory of stimulated absorption and emission with account of different probabilities of these processes in the presence of quantum recoil. The presence of a medium allows one to prolong the synchronism condition by changing the density of medium along the electron path, leaving the ondulator parameters unchanged. And what is more, the medium, decreasing the phase velocity of light, increases the phase space of interaction, which essentially increases the efficiency of acceleration. The effect of medium on acceleration manifests itself best in the MeV range of electron energy. 13 refs.