Abstract: Acceleration of electrons or charged particles by a linearly polarized electromagnetic wave (LPEMW) propagating in a medium along an external magnetic field is theoretically studied. We have investigated three acceleration cases here: (Ⅰ) the medium's refractive index changes with location but the external magnetic field is constant, (Ⅱ) the medium's refractive index is constant but the external magnetic field increases with the distance in the wave propagation direction, and (Ⅲ) both the medium's refractive index and the external magnetic field change with the distance. The results show that the most efficient (i.e., at a fixed acceleration distance, obtaining the highest relativistic factor) electron acceleration by the LPEMW can be fulfilled in case (Ⅲ). Besides, in case (Ⅲ), the drawback (such as charged particles' going backward for a while) in the acceleration of case (Ⅱ) can be avoided or greatly reduced, which is very important for acceleration of a bunch of electrons or charged particles by LPEMW. It is believed that the acceleration mechanism found in case (Ⅲ) can be helpful in the design of a compact and efficient chargedparticle accelerator.