A novel method named tensor global-local structure analysis (TGLSA) is proposed for batch process monitoring. Different from principal component analysis (PCA) and locality preserving projections (LPP), TGLSA aims at preserving both global and local structures of data. Consequently, TGLSA has the ability to extract more meaningful information from data than PCA and LPP. Moreover, the tensor-based projection strategy makes TGLSA more applicable for the three-dimensional data than multiway-based methods, such as MPCA and MLPP. A TGLSA-based online monitoring approach is developed by combining TGLSA with a moving window technique. Two new statistics, i.e., SPD and R-2 statistics, are constructed for fault detection and diagnosis. In particular, the R-2 statistic is a novel monitoring statistic, which is proposed based on a support tensor domain description method. The effectiveness and advantages of the TGLSA-based monitoring approach are illustrated by a benchmark fed-batch penicillin fermentation process.