Particles with low energy can not be accelerated only with harmonic number of 1 because of a restriction of the frequency range of the CSRm RF cavities with 0.25 to 1.7 MHz. This paper just simulated and studied the beam acceleration process of HIRFL-CSR. By means of changing harmonic, i.e. particles were captured and aecelerated to some energy with harmonic number of 2 first and then to the final energy with harmonic number of 1. The main RF parameters of CSRm and some beam parameters are given according to the simulation. In addition, the changing of particle distribution in longitudinal phase space during the accelerating process has been obtained.