On the basis of analyzing the principle of multicarrier code division multiple access (MC-CDMA), an optimized complex wavelet packet based MC-CDMA system (CWP-MC-CDMA) is proposed. The system performances with equal gain combining (EGC) technique and maximum ratio combining (MRC) technique in Nakagami-m fading channels are investigated, respectively; and the corresponding bit error rate (BER) expression is derived. The system can overcome the decrease of spectrum efficiency of discrete Fourier transform (DFT) based conventional MC-CDMA (DFT-MC-CDMA) due to inserting a cyclic prefix (CP). Theoretical analysis and simulation results show that the CWP-MC-CDMA system outperforms DFT-MC-CDMA as well as the real wavelet packet based MC-CDMA (RWP-MC-CDMA) system, and has superior ability to combat multi-path fading and multi-access interference (MAI). Moreover, the BER performance of the proposed system is also superior to that of the conventional MC-CDMA with CP.