In this paper, we propose an efficient regularized zero-forcing (RZF) precoding method that has lower hardware resource requirements and produces a shorter delay to the first transmitted symbol compared with truncated polynomial expansion (TPE) that is based on Neumann series in massive multiple-input multiple-output (MIMO) systems. The proposed precoding scheme, named matrix decomposition-polynomial expansion (MDPE), essentially applies a matrix decomposition algorithm based on polynomial expansion to significantly reduce full matrix multiplication computational complexity. Accordingly, it is suitable for real-time hardware implementations and high-mobility scenarios. Furthermore, the proposed method provides a simple expression that links the optimization coefficients to the ratio of BS/UTs antennas (β). This approach can speed-up the convergence to the matrix inverse by a matrix polynomial with small terms and further reduce computation costs. Simulation results show that the MDPE scheme can rapidly approximate the performance of the full precision RZF and optimal TPE algorithm, while adaptively selecting matrix polynomial terms in accordance with the different β and SNR situations. It thereby obtains a high average achievable rate of the UTs under power allocation.