Millimeter wave (mmWave) and massive multiple input multiple output (MIMO) are recognized as key technologies in the forthcoming beyond the fifth-generation (B5G) and the sixth-generation (6G) wireless networks. In this paper, a multibeam MIMO non-orthogonal multiple access (NOMA) scheme with weighted beam superposition for mmWave is proposed to enhance the system sum rate while ensuring fairness of users as much as possible. Specifically, a method of power allocation is adopted to guarantee the minimum demanded for the quality of service (QoS) of the weak users (lower channel gain)in each group. Furthermore, to improve further the sum rate after the QoS of the weak users is satisfied, the coefficient of strong users' beam gain are set to the largest value. In system simulations, we compare the performance of three multi-beam schemes, i.e, beam splitting, beam superposition and the proposed scheme, together with a single beam scheme, and a TDMA scheme at different levels of the SNR. The simulation results demonstrate that the system sum rate of the proposed method is much higher than TDMA scheme and competitive compared to the best scheme.