The development in information technology has resulted in more diverse data characteristics and a larger data scale. Therefore, pattern recognition techniques have received significant interest in various fields. In this study, we focus on a pattern recognition technique based on distance metric learning, which is known as the learning method in metric matrix under an arbitrary constraint from the training data. This method can acquire the distance structure, which takes account of the statistical characteristics of the training data. Most distance metric learning methods estimate the metric matrix from pairs of training data. One of the problem of the distance metric learning is that the computational complexity for prediction (i. e. distance calculation) is relatively high especially when the dimension of input data becomes large. To calculate the distance effectively, we propose the way to derive low rank metric matrix with nuclear norm regularization. When solving the optimization problem, we use the alternating direction method of multiplier and proximal gradient. To verify the effectiveness of our proposed method from the viewpoint of classification accuracy and rank reduction, simulation experiments using benchmark data sets are conducted.