Unsupervised person re-identification(person Re-ID) based on traditional asymmetric metric learning faces the problems of data distribution differences and feature nonlinearity caused by uncontrolled collection of pedestrian images. To solve these problems, an unsupervised person re-identification method based on asymmetric metric learning with kernel distribution constraints is proposed. Firstly, the data distribution constraint is introduced into asymmetric metric learning, and the mean difference between samples is calculated by using the maximum mean difference term. This metric method effectively overcomes the problem of distribution differences in different sample data features caused by scene changes. Secondly, the Gaussian kernel function is introduced into asymmetric metric learning based on data distribution constraints, and pedestrian samples are mapped to high-dimensional space through nonlinear mapping. This method overcomes the problem of linear inseparability of pedestrian features, while avoiding the high dimensionality of features and reducing computational complexity. Finally, the optimal metric matrix is obtained by solving the generalized eigenvalue problem. Extensive experiments are conducted on five datasets: VIPeR, PRID450S, CHUK01, Market-1501, and DukeMTMC-reID. The experimental results of comparison with other methods show that our method achieves competitive performance.