Abstract-The wireless devices will rapidly growth with the application of the Internet of Thing (IoT), which results in the huge power consumption. To realize the green communication, in this paper, we study the energy efficiency (EE) problem in a non-orthogonal multiple access (NOMA)-based CRAN, where microwave and millimeter wave (mmWave) are applied in fronthaul and access links, respectively. Based on this, we formulate the power optimization problem to maximize the EE of the system subject to the fronthaul capacity and transmit power constraints. Due to the formulated problem is nonconvex, we first transform the fractional objective function into the subtractive form. After that, an algorithm containing outer and inner loops is proposed to deal with this non-convex problem. In particular, in the outer loop, the 1 -norm technique is adopted to transform the nonconvex fronthaul capacity constraint into the convex one; while in the inner loop, the weighted minimum mean square error (WMMSE) approach is applied to solve the formulated problem. Simulation results demonstrate that the proposed NOMA scheme can obtain higher EE as well as throughput in comparison with the conventional orthogonal multiple access (OMA) scheme.