In coherent optical communication transmission systems based on higher-order modulation, the signal at the receiver side is subject to phase noise interference, which has a direct impact on the system performance. The conventional blind phase search (BPS) algorithm has high line tolerance and is suitable for a variety of modulation formats. However, as the modulation order increases, the number of test phase used for BPS will sharply increase. A new low-complexity carrier phase estimation (CPE) algorithm is proposed in this work for M-ary quadrature amplitude modulation (M-QAM) format. Firstly, the relationship between the B test phase and the average Euclidean distance is obtained using the BPS algorithm. Then, a carrier phase estimation based on a two-stage BPS with cubic spline interpolation (CSI) is proposed, and the smooth curve relationship between the (2B-1) equally spaced interpolated phase and the average Euclidean distance is obtained. Finally, the phase value corresponding to the minimum of the curve is taken as the optimal phase estimation value. The simulation results show that with a small number of test phases, the carrier phase can be effectively recovered by the CSI algorithm, and compared with that of the BPS algorithm, the computational complexity of multiplier and additive of the CSI algorithm is reduced by 38% and 42% (16-QAM) respectively, which provides a new idea for carrier phase recovery.