A phase noise suppression algorithm based on real-imaginary-alternate pilots was proposed for a coherent optical orthogonal frequency division multiplexing communication system with offset quadrature amplitude modulation (CO-OFDM-OQAM). The algorithm uses the properties of laser phase noise and the intrinsic imaginary interference (IMI) symmetry law to design real-imaginary-alternate pilots. In combination with a linear fitting, it can accurately estimate the common phase error (CPE) for CO-OFDM-OQAM. As the compensation was performed in the frequency domain, the computational complexity was significantly reduced compared to the time-domain phase noise suppression algorithms. A numerical simulation platform was built for a polarization multiplexed CO-OFDM-OQAM system with an effective bit rate of 65 GBits/s. Through it, the transmission performance of the system with different laser linewidths and numbers of subcarriers was studied, and the suppression effect of the proposed method on phase noise was examined. The results obtained confirm that the linewidths required to reach the FEC limit for BER are equal to 801.1, 349, and 138.4 kHz for a fixed OSNR of 25 dB and a total number of subcarriers of 256, 512, and 1024, respectively. For the system using a 16-QAM modulation format with 256 or 512 subcarriers, it compensates well for the laser phase noise without affecting the power peak-to-average ratio.