In this letter, we consider non-orthogonal multiple access (NOMA) applying into massive multiple input multiple output (mMIMO) low earth orbit (LEO) satellite communication system (SCS) to improve spectral efficiency. Specifically, we investigate sum rate maximization problem with transmit power, quality of service (QoS) constraints, imperfect successive interference cancelation (SIC) and imperfect channel state information (CSI) considered. We decouple the original problem into two parts: precoding vectors design and transmit power optimization. Precoding vectors are derived for maximizing the average signal power in each beam and eliminating inter-beam interference (IBI). Then, transmit power optimization problem is transformed into a convex optimization problem by utilizing the first order Taylor expansion, an iterative algorithm is proposed to get the optimal sum rate. Finally, simulation results verify the convergence of the proposed algorithm and our proposed mMIMO NOMA approach is better than other approaches.