Usually, multiple secondary users (SUs) utilize the opportunistic spectrum access (OSA) in cognitive radio networks to communicate with the secondary base station (sBS). In uplink transmission, each SU can only select one channel from C primary channels to sense, access, and transmit data packets with the constraints of hardware and energy. Distributed non-orthogonal multiple access-based multi-armed bandit (D-NOMA-MAB) approach is proposed to solve the problem of the channel selection and the power level selection, which alleviates the impact of the collision in the same channel. D-NOMA-MAB approach improves the energy efficiency of the system and the successful transmission probability obviously by introducing 2-D selection for the arms and the factor of energy efficiency in the policy index of the restless MAB problem.