Fault detection is fundamental to many industrial applications. With the development of system complexity, the number of sensors is increasing, which makes traditional fault detection methods lose efficiency. Metric learning is an efficient way to build the relationship between feature vectors with the categories of instances. In this paper, we firstly propose a metric learning-based fault detection framework in fault detection. Meanwhile, a novel feature extraction method based on wavelet transform is used to obtain the feature vector from detection signals. Experiments on Tennessee Eastman (TE) chemical process datasets demonstrate that the proposed method has a better performance when comparing with existing methods, for example, principal component analysis (PCA) and fisher discriminate analysis (FDA).