Nonlinear partial least-squares (NPLS) is widely used in quality-relevant process control and fault diagnosis for strongly nonlinear systems; however, the existing NPLS approaches suffer from various disadvantages. This study proposes a novel statistical model based on locality-preserving partial least squares (LPPLS) to enhance the processing capacity for system nonlinearity. The main concept of the LPPLS model is to utilize the locality-preserving projection to extract the principal components and preserve nonlinearities within the partial least squares (PLS) process. The intuitive presentations for three types of LPPLS models are established within the proposed framework for strongly nonlinear systems, in which the process variables can correlate nonlinearly with each other and with the quality variables simultaneously. A canonical algorithm, which is easily applied in actual processes and is similar to the traditional linear PLS, is deduced to extract the principal components. Then,, a quality-related monitoring strategy is established based on the LPPLS model. The experimental results from an artificial test data set and the Tennessee Eastman process (TEP) benchmark demonstrate that the proposed method can maintain as much of the local properties of the original data as possible and yield good monitoring results for quality-relevant faults.