Four wave mixing (FWM) is a nonlinear process in which three waves of frequency f_p, f_q and f_r interact through the third order nonlinear susceptibility of optical fiber to generate a new wave of frequency f_{pqr} = f_p + f_q - f_r. Studies so far have mainly concentrated on its impact on multichannel transmission. For example, in wavelength division multiplexing (WDM) system, FWM phenomenon will cause crosstalk among channels, which degrades the system performance. Two-dimensional (2-D) optical code-division multiple-access (OCDMA) system uses multiple-wavelength signal. Therefore, the system performance is also affected by FWM phenomenon. The object of our study is to comprehensively analyze the performance degradation of 2-D OCDMA system due to FWM phenomenon. Various parameters will be investigated including power limit, power penalty, and the number of supportable users.