For the problem that the principal component vector obtained by Principal Component Analysis (PCA) algorithm is not sparse enough and has many non-zero elements, PCA algorithm was optimized by the reweighting method, and a new method for extracting high-dimensional data features was proposed, namely Reweighted Sparse Principal Component Analysis (RSPCA) algorithm. Firstly, the reweighted l ₁ optimization framework and LASSO (Least Absolute Shrinkage and Selection Operator) regression model were introduced into PCA algorithm to establish a new dimensionality reduction model. Then, the model was solved by using alternat minimization algorithm, singular value decomposition algorithm and minimum angle regression algorithm. Finally, the face recognition experiment was carried out to verify the effectiveness of the algorithm. In the experiment, the K-fold cross-validation method was used to realize the recognition experiment on the ORL face dataset by using PCA algorithm and RSPCA algorithm. The experimental results show that RSCPA algorithm can obtain sparser vector while performs as good as PCA algorithm, has the average recognition accuracy reached 95.1%, which is increased by 6.2 percentage points compared with that of the best performing algorithm sPCA-rSVD (sparse PCA via regularized SVD). And in the experiment of the real-world specific practical application handwritten digit recognition, RSPCA algorithm has the average recognition accuracy of 96.4%, The superiority of the proposed algorithm in face recognition and handwritten digit recognition was proved.