The optimal energy efficient power allocation is investigated for the uplink multi-carrier non-orthogonal multiple access (MC-NOMA) system. Considering the user fairness, the power allocation is formulated as a maximization problem of the system weighted energy efficiency, which is defined as a ratio of the weighted sum rate to the total power consumption. By utilizing Dinkelbach algorithm and Lagrange dual decomposition approach, the optimal closed-form power allocation expressions are derived. The convergence and optimality of the proposed scheme can be proved. The simulation results demonstrate performance enhancement of the proposed algorithm compared to the existing works, i.e., the enhance water-filling scheme and orthogonal multiple access (OMA) system.