A low complexity carrier phase estimation (CPE) algorithm for M-ary quadrature amplitude modulation (m-QAM) optical communication systems is investigated in this paper. In the proposed CPE algorithm, a two-stage CPE method is adopted. In the first stage, the QPSK points of the constellation are picked out to achieve a coarse phase estimation using the traditional Viterbi and Viterbi algorithm. In the second stage, all the points of the constellation are used for a fine phase estimation. In addition, the fourth-power operation is replaced by the 4-level absolute operation for the removal of mod...