Abstract: In traditional supervised learning, each object is represented by a single instance and associated with only one class label. Recently, multi-label learning attracts much attention from researchers of machine learning, pattern recognition etc., due to its ability in obtain more information on predicting multiple class labels. In multi-label learning, each object is represented by an instance, while it may be assigned to multiple class labels simultaneously. Hence, its task is to predict a class label set for the unknown instance. The resulting model is usually an ill-conditioned quadratic program, which requires regularization. In this paper, a multi-label classification algorithm based on regularized least squares classification is proposed, which is derived from the traditional regularized least squares classification. To establish our model, we first transform the multi-label learning problem into a multiple independent binary classification problem (each for one class label). Then, in order to fully exploit the class label correlations information, an adjacent graph based on all the class labels is built, where each node stands for one class label and the weight of each edge reflects the similarity between corresponding pairwise-label. Finally, a multi-label regularized least squares model is constructed on the basis of kernel function, whose first order optimality condition is a Sylvester equation, which can be solved efficiently by using numerical linear algebra technique. We perform experiment on eight benchmark data sets in terms of five different evaluation criteria and compare it with the other six state-of-the-art multi-label learning algorithms. The results show that our algorithm is competitive.