In this paper, we analyze the bit error rate (BER) performance of optical code division multiple access (CDMA) system based on the optical zero-correlation zone (ZCZ) code using the optical correlator which is called optical ZCZ-CDMA system, over the optical fiber and space by theoretical formula. In the optical fiber transmission of this system, the effect of the avalanche photodiode (APD) noise, thermal noise and co-channel interference are considered. Additionally, the effects of the scintillation and background noise are considered in the optical space transmission of this system. The optical ZCZ code, which is a set of pairs of a binary sequence consisting of 1 or 0 and a biphase sequence consisting of 1 or -1 with zero-correlation zone, may be able to provide optical CDMA communication system suppressed co-channel interference. As a result, the BER performance of optical ZCZ-CDMA system over the optical space go down compared to that over the optical fiber, and this system can't remove completely co-channel interference.