We propose a new multiple access communication system based on finite field wavelet spread signature (FFWSS). In addition to the function of frequency diversity and multiple access, which are typically provided by traditional spreading codes, the FFWSS spreads data symbols in time, resulting in robustness against frequency selective slow fading. Using the FFWSS to spread a data symbol so that it is overlapped with neighboring symbols, a FFWSS-CDMA system is developed. It is observed that the ratio of the maximum nontrivial value of periodic correlation function to the code length of FFWSS is the same as that of a Sidelnikov sequence. Using RAKE-based receivers, simulation results show that the proposed FFWSS-CDMA system yields lower bit error rate (BER) than conventional DS-CDMA and MT-CDMA systems in multipath fading channels.