Orthogonal Frequency Division Multiplexing (OFDM) is characterized by its high data rate. However, the modulation method used in the system is subject to the influence of phase noise due to the need of time synchronization. In this paper, an algorithm based on MMSE (minimum mean square error) is developed to compensate the influence of both the common phase error (CPE) and inter carrier interference (ICI), which are two aspects of phase noise, under common Gaussian white noise. The result of noise cancellation is presented in signal-to-noise ratio (SNR) and symbol error rate (SER). Like digital signal in general, SNR can reduce SER with or without phase noise compensation. The compensation of phase noise significantly reduces the SER of the decoded signal. However, the bandwidth of phase noise still determines the signal accuracy. Under high bandwidth of phase noise, increasing SNR will only slightly increase SER, which is not efficient.