A fast-convergence singular value decomposition (SVD) algorithm is developed for tracking time-varying channels in massive MIMO precoding/beamforming systems. Since only strong eigen-modes are selected for data transmission in these systems, our SVD algorithm exploits the properties of partial decomposition and temporal correlation. Besides, the proposed self-adjusting inverse power method can achieve fast convergence by modifying the shift according to the intermediate result during each iteration. Furthermore, the singular vectors and values of the desired eigenmodes can be computed simultaneously. Thus, parallel processing is possible to facilitate high-throughput implementation. Compared to the self-power method with super linear convergence, the self-adjusting inverse power method has better convergence and lower complexity. Good channel tracking capability is also demonstrated.