In this paper, Interference-Cancelled CDMA system using binary ZCD spreading codes is introduced. Proposed Interference-Cancelled CDMA system can be usefully used for the intra-cellular Interference-Cancelled wireless communication systems. Binary ZCD spreading code sets have various sequence period and family sizes and the ZCD properties of them are very effective for Interference-cancelled CDMA Systems. In this paper, we mathematically analyzed the system performance of our proposed Interference-Cancelled CDMA system in the AWGN channel and various interference environments such as MAI and MPI. Furthermore, using the BER performance simulation we certify the available interference cancellation properties of the proposed system.