To achieve the maximum network energy efficiency (EE) and guarantee the fairness of EE among cognitive users (CUs), respectively, in the massive multiple-input multiple-output (MIMO) cognitive radio network (CRN), we investigate two power optimization problems, i.e., network EE optimization problem (NEP) and fair EE optimization problem (FEP) under a practical power consumption model. Due to the fractional nature of EE and the interference, both NEP and FEP are nonconvex and NP-hard. In order to tackle these issues, we propose two energy-efficient power control algorithms, in which we decompose NEP/FEP into two steps, and solve them with an alternating iterative optimization scheme. Specifically, in the first step, for an initial transmit power, the maximum network EE/fair EE is achieved by the bisection method based on fractional programming; then with the achieved EE, in the second step, the adapted optimal transmit power can be obtained by an efficient iterative algorithm based on sequential convex programming; these two steps are performed alternately until the stop conditions are reached. Numerical results confirm the fast convergence of these proposed algorithms, and demonstrate their effectiveness with high network EE and well fairness of EE among CUs. Furthermore, it is illustrated that, under a practical power consumption model, more cognitive base station (CBS) antennas would cause some loss of network EE but bring some improvements on the network spectral efficiency (SE), while higher circuit power consumption would reduce the network EE but only slightly affect the network SE.