Metric, also called distance function, is a special function in metric space that satisfies certain conditions. It is generally used to reflect some important distance relationships between data examples. Since distance has a great influence on various classification and clustering problems, metric learning has an important influence on these machine learning problems. Existing metric learning algorithms for classification problems are vulnerable to noise, the classification accuracy is not stable and tends to fluctuate. To solve this problem, this paper presents a robust metric learning algorithm based on maximum correntropy criterion. The core of maximum correntropy criterion is Gaussian kernel function, which is introduced into metric learning in this study. We construct a loss function with Gaussian kernel function and optimize the objective function using gradient descent method. The output metric matrix is computed through repeatedly testing and adjusting the parameters. The metric matrix learned through this method will have better robustness and will effectively improve the classification accuracy when dealing with various classification problems affected by noise. This study performs validation experiments on some popular machine learning datasets (UCI) and face datasets.