A novel dimensionality reduction algorithm named "global-local preserving projections" (GLPP) is proposed. Different from locality preserving projections (LPP) and principal component analysis (PCA), GLPP aims at preserving both global and local structures of the data set by solving a dual-objective optimization function. A weighted coefficient is introduced to adjust the trade-off between global and local structures, and an efficient selection strategy of this parameter is proposed. Compared with PCA and LPP, GLPP is more general and flexible in practical applications. Both LPP and PCA can be interpreted under the GLPP framework. A GLPP-based online process monitoring approach is then developed. Two monitoring statistics, i.e., D and Q statistics, are constructed for fault detection and diagnosis. The case study on the Tennessee Eastman process illustrates the effectiveness and advantages of the GLPP-based monitoring method.