We study new modulation classification methods for M-ary CPM signals based on the average likelihood ratio test (ALRT) approach. It is well-known that the M-ary CPM signal can be decomposed into the superposition of multiple PAM waveforms. In this paper, we apply the decomposed PAM waveforms for CPM classification through ALRT. However, to detect the CPM signals costs a high complexity because the PAM decomposition method requires multiple filters to match the PAM waveforms. Hence, we propose a new phase detection method which has lower complexity. In addition, we analyze the phase noise in the phase detection method to insure the prerequisite of applying the ALRT approach for modulation classification. Simulation results show that the new M-ary CPM classification method has satisfying probability of correct classification when SNR is beyond 0 dB.