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In this paper, a novel communication system is introduced, i.e., the frequency-hopping multiple-access OFDM-BPSK communication system. Based on characteristic function method, the bit error rate (BER) performance of the system is derived in additive white Gaussian noise (AWGN) and Rayleigh fading channels. The numerical results firstly indicate the relationship between BER and the parameters such as the size of frequency slots set Nu, the number of OFDM subcarriers N and the number of users Nu. By the numerical and simulation results, the frequency resource of OFDM-BPSK-FHMA system is saved and the BER is decreased under the same parameter compared with other similar communication systems.