In this paper, the energy efficiency maximization problem is tackled in a multiple-input multiple-output (MIMO)-non-orthogonal multiple access (NOMA) heterogeneous cellular network (HCN) with Internet of Things (IoT) for wireless communication systems. A fractional non-convex optimization problem is formulated to maximizes the energy efficiency (EE) subject to the transmit power constraints and the minimum rate requirement for the cell edge (CE) users present in both macro base station (MBS) and pico base station (PBS). The above problem is hard to solve due to its nonlinear fractional objective function. Fractional programming properties is firstly employed to convert the non-convex problem into its parametric form. In addition, an efficient iterative algorithm is proposed established on the branch and reduced bound (BRB) approach that achieves convergence to the above problem, mitigates the inter tier interference and also improves the fairness between the users. Comprehensive numerical results emphasize that the proposed scheme achieves higher energy efficiency as compared with the existing NOMA scheme and the conventional orthogonal multiple access (OMA) scheme.