Abstract: Non-orthogonal multiple access (NOMA) has become the key technology in 5G communication. NOMA can achieve multi-user multiplexing in transmit power domain by allocating different power, which can effectively improve the system capacity and the spectral efficiency. Different power allocation schemes will directly affect the throughput of the system. Therefore, in order to increase the system capacity, it is necessary to study an effective power allocation scheme. Aiming at the local optimal problem of NOMA downlink power allocation algorithm, an optimal power allocation scheme using conjugate gradient method is proposed， which is used to solve the user's maximum weighted sum rate. The existing theory proves that the conjugate gradient method can converge to the global optimal solution. The simulation results show that its performance is better than fixed power allocation (FPA) algorithm’s and fractional transmit power allocation (FTPA) algorithm’s, and NOMA system with this method is better than orthogonal multiple access (OMA) system.