Non-orthogonal multiple access (NOMA) and heterogeneous network (HetNet) are two significant and promising enabling techniques to further improve overall system performance for nextgeneration mobile communication systems. In this paper, we develop a novel NOMA HetNet through applying NOMA technique to both macrocell and small-cell of conventional HetNet, which improves the spectral efficiency whereas results in a more complex interference environment. To tackle this complicated interference problem and maximize the overall throughput of this NOMA HetNet, meanwhile ensure the desired quality of service (QoS) of each user, we mathematically formulate a power allocation problem which proves to be an NP-hard problem. Then, to deal with this optimization problem, we propose a users scheduling scheme and an iterative distributed power control algorithm. The simulation results demonstrate that compared with the conventional orthogonal multiple access (OMA) HetNet systems and single-tier NOMA networks, the combination of OMA technique and HetNet with the proposed algorithm can greatly improve the system performance in terms of spectral efficiency and outage performance.