We propose a phase-noise compensation algorithm by using radio frequency pilot (RF-Pilot) method in combination with extend Kalman filter (EKF) in time domain for the coherent optical orthogonal frequency division multiplexing (CO-OFDM) system with large linewidths and high-order circular quadrature amplitude modulation (C-QAM). We realize the coarse phase-noise compensation in time domain by setting a RF-Pilot at the receiver, and then complete the channel evaluation and channel balance. After accomplishing the initial pre-decision in the frequency domain, we use EKF to realize the final phase noise compensation, according to the judged temporal signal and the channel equalization temporal signal. We numerically verify the algorithm by transforming in a 50 Gb·s -1 CO-OFDM system with 100 km transmission distance under C-16QAM and C-32QAM. The results show that compared with original RF-Pilot phase-noise compensation algorithms, the proposed method has better performance on the phase noise compensation while has no obvious decrease of frequency utilization, and the complexity is not increased significantly. For CO-OFDM systems with C-32QAM and a laser linewidth of 2.1 MHz, the bit error rate achieves the upper limit of forward error correction. It theoretically confirms that the proposed algorithm can improve the tolerance of laser linewidth on the CO-OFDM system. We can use the inexpensive distributed feedback lasers with relatively large linewidth as the source of the object and the oscillator of the receiver. The proposed phase-noise compensation algorithm is beneficial to the application of CO-OFDM system in long distance access network and metropolitan area network.