Abstract: Locality preserving projections, which preserve the neighborhood relationship of data, has been successfully applied in process monitoring. However, these methods neglect non-locality structure information and cannot guarantee the relationship of samples faraway. Locality preserving sparse modeling proposed recently use sparse coding to get a set of overcomplete basis, and well-represented inherent structural features from the raw data. Owing to sparse coding for learning local sparse structure features and representing raw data appropriately, we propose non-locality-constrained locality sparse preserving projections. First, we extract the sparse code and represent the global structure information by using sparse coding; second, we preserve the locality structure characteristics with non-locality relationship constraint, and estimate the probability densities of different sparse codes, which are set up with different weighting values to evaluate their contribution to faults; then, we build a combined statistical index for fault detection based on process status; Finally, we validate the proposed method using a numerical study and the Tennessee Eastman benchmark process, and compare it with several models. The monitoring results indicate its superior performance.