A novel suppression method of the phase noise is proposed to reduce the negative impacts of phase noise in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The method integrates the sub-symbol second-order polynomial interpolation (SSPI) with cubature Kalman filter (CKF) to improve the precision and effectiveness of the data processing through using a three-stage processing approach of phase noise. First of all, the phase noise values in OFDM symbols are calculated by using pilot symbols. Then, second-order Newton interpolation (SNI) is used in second-order interpolation to acquire precise noise estimation. Afterwards, every OFDM symbol is partitioned into several sub-symbols, and second-order polynomial interpolation (SPI) is utilized in the time domain to enhance suppression accuracy and time resolution. Ultimately, CKF is employed to suppress the residual phase noise. The simulation results show that this method significantly suppresses the impact of the phase noise on the system, and the error floors can be decreased at the condition of 16 quadrature amplitude modulation (16QAM) and 32QAM. The proposed method can greatly improve the CO-OFDM system's ability to tolerate the wider laser linewidth. This method, compared to the linear interpolation sub-symbol common phase error compensation (LI-SCPEC) and Lagrange interpolation and extended Kalman filter (LRI-EKF) algorithms, has superior suppression effect.