In high-speed optical communication, the blind phase search (BPS) algorithm performs carrier phase estimation better but with higher computational complexity (CC), bringing a larger computational burden to the digital signal processing unit. In this paper, a new low-complexity CPE algorithm (DBPS) is proposed for M-ary quadrature amplitude modulation (M-QAM) formats. It uses the BPS algorithm to estimate the compensation phase interval, before using dichotomy to quickly and accurately determine the compensation phase value. Simulation results show the CC (multiplication / addition) of DBPS is reduced by 2.79 / 2.84 (16-QAM), 5.35 / 5.45 (64-QAM), and 2.98 / 3.01 (128-QAM) than that of BPS, and DBPS has a smaller phase tracking error variance. DBPS can relax the limitation of optical communication rate caused by high-speed data operations.