Abstract: Reduced rank estimation using penalty functions to restrict ranks of variety matrices is often used for solving the multi-collinearity of high-dimensional multivariate regression. Here a hard-thresholding singular value penalization was considered to get more efficient results. Through local linear approximate method, non-convex models were converted to computable ones. This model is computationally efficient, and the resulting solution path is continuous. Experiment results from simulation and public datasets show that this kind of reduced rank regression has better accuracy than some frequently-used ones in most situations.