A scenario where one ’dumb’ radio and multiple cognitive radios communicating simultaneously with a common receiver is considered. In this paper, we derive an achievable rate region of the multiple-user cognitive multiple-access channel (MUCMAC) under both additive white Gaussian noise (AWGN) channel and rayleigh fading channel, by using a combination of multiple user dirty paper coding (DPC) and superposition coding. Through cognition, it is assumed that the secondary users (SUs) are able to obtain the message of the primary user (PU) non-causally beforehand. Using this side information, the SUs can perform multiple user DPC to avoid the interference from the SU. Besides, the SUs can also allocate part of their transmit power to aid the PU, using superposition coding. Therefore, the capacity region of traditional multiple-access channel (MAC) can be enlarged. Moreover, some asymptotic results are shown as the number of SUs increases. In the AWGN case, it is illustrated that the maximum achievable rate of the PU grows logarithmically with the increase of the number of SUs, whereas in the Rayleigh case, we show that the cognitive gain will increase with the decreasing of the channel signal to noise ratio (SNR). A this scenario where one ’dumb’ radio and multiple cognitive radios communicating simultaneously with a common receiver is considered. In this paper, we derive an achievable rate region of the multiple-user cognitive multiple-access channel (MUCMAC) under both additive white Gaussian noise (AWGN) channel and rayleigh fading channel, by using a combination of multiple user dirty paper coding (DPC) and superposition coding. It is assumed that the secondary users (SUs) are able to obtain the message of the primary user ( PU) non-causally beforehand. Using this side information, the SUs can perform multiple user DPC to avoid the interference from the SU. the capacity region of traditional multiple-access channel (MAC) can be enlarged. Moreover, some asymptotic results are shown as the number of SUs increases. In the AWGN case, it is illustrated that the maximu m achievable rate of the PU grows logarithmically with the increase of the number of SUs, while in the Rayleigh case, we show that the cognitive gain will increase with the decreasing of the channel signal to noise ratio (SNR).