Fault diagnosis algorithms based on neighborhood preserving embedding (NPE) have been widely used because they can effectively extract local information of the process. However, typical NPE method is sensitive to parameter selection and outliers, while ignoring the global information of process data. Therefore, a fault diagnosis algorithm based on robust low rank adaptive neighborhood preserving embedding (RLANPE) is proposed. This method integrates adaptive neighborhood embedding, projection learning and low rank representation into a framework, which can effectively extract local information of data while obtaining global optimal solution. In order to explore the global information of the data and eliminate the influence of outliers, low rank constraint is imposed on RLANPE to further enhance the information extraction capability. Meanwhile, RLANPE introduces projection constraints based on norm to select the most discriminative features. Finally, the solution process and computational complexity analysis are given. The better dimension reduction performance and structure preservation capability of the proposed method are verified by three synthetic data sets. The average fault detection rate in Tennessee Eastman can reach 83.72%, which is nearly 3% higher than that of the comparison algorithms.