The traditional feature selection methods always remove redundant features by using correlation measures, and it is not considered that there is a large amount of noise in a high-dimensional correlation matrix, which seriously affects the feature selection result. In order to solve the problem, a feature selection method based on Random Matrix Theory (RMT) was proposed. Firstly, the singular values of a correlation matrix which met the random matrix prediction were removed, thereby the denoised correlation matrix and the number of selected features were obtained. Then, the singular value decomposition was performed on the denoised correlation matrix, and the correlation between feature and class was obtained by decomposed matrix. Finally, the feature selection was accomplished according to the correlation between feature and class and the redundancy between features. In addition, a feature selection optimization method was proposed, which furtherly optimize the result by comparing the difference between singular value vector and original singular value vector and setting each feature as a random variable in turn. The classification experimental results show that the proposed method can effectively improve the classification accuracy and reduce the training data scale.