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This paper presents the study on Wavelet transform based Multicarrier Code Division Multiple Access (MC-CDMA) system for a downlink wireless channel. The performance of the system is studied for Additive White Gaussian Noise Channel (AWGN) and slowly varying multipath channels. The bit error rate (BER) versus Signal to Noise ratio (SNR) is used as a performance measure using simulation done on computer. Comparison of the simulated results with the theoretical limit of a BPSK modulated signal shows that this system performs near the theoretical limit for both A WGN and slowly varying Flat fading channel. Also, a comparison with the Discrete Fourier Transform (DFT) based system was made for A WGN channel and the result shows that even in the absence of a guard interval, the wavelet based system performs equally with the DFT.