In this paper, the joint design of user clustering and power allocation is investigated in a downlink non-orthogonal multiple access based millimeter wave (mmWave-NOMA) system. In order to maximize the sum rate of the system, the Stackelberg game based optimization problem is formulated. With the aid of game theory, a low complexity algorithm is proposed to dynamically allocate users into different clusters. By deriving the closed-form expressions, the optimal power allocation coefficients of the users in each cluster are obtained. The properties of the proposed joint algorithm, including complexity, convergence and stability, are analyzed. Simulation results demonstrate that: i) the proposed algorithm can significantly improve the sum rate and reduce the outage probability of the mmWave- NOMA system; ii) the application of NOMA in mmWave systems is capable of achieving promising gains over conventional orthogonal multiple access (OMA) based frameworks in both cases.