Power allocation plays a crucial role in wireless communications. To facilitate the efficient allocation of limited transmit power, in this paper, a bit error rate (BER) constraint based power allocation scheme is proposed for the downlink of multi-carrier code division multiple access (MC-CDMA) systems with linear minimum mean square error (MMSE) receiver. According to the instantaneous path gains, the proposed scheme can determine the required minimum transmit power on each channel to meet the BER constraint. The simulation results show that the proposed scheme can consistently provide high-quality solutions with a very few iteration time, and also prove that it is efficient in reducing the transmit power while meeting BER constraint, and thereby improves the system performance.