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As energy efficiency (EE) is a key performance indicator for the future wireless network, it has become a significant research field in communication networks. In this paper, we consider multi-cell multi-carrier non-orthogonal multiple access (MCMC-NOMA) networks and investigate the EE maximization problem. As the EE maximization is a mixed-integer nonlinear programming NP-hard problem, it is difficult to solve directly by traditional optimization such as convex optimization. To handle the EE maximization problem, we decouple it into two subproblems. The first subproblem is user association, where we design a matching-based framework to perform the user association and the subcarriers’ assignment. The second subproblem is the power allocation problem for each user to maximize the EE of the systems. Since the EE maximization problem is still non-convex with respect to the power domain, we propose a two stage quadratic transform with both a single ratio quadratic and multidimensional quadratic transform to convert it into an equivalent convex optimization problem. The power allocation is obtained by iteratively solving the convex problem. Finally, the numerical results demonstrate that the proposed method could achieve better EE compared to existing approaches for non-orthogonal multiple access (NOMA) and considerably outperforms the fractional transmit power control (FTPC) scheme for orthogonal multiple access (OMA).