In this paper, the GTucker2 model is proposed for monitoring both even lentgh and uneven-length batch processes. The GTucker2 model has two pominent advantages. The first one is that it performs tensor decomposition on the three-way data array and thus avoids potential problems of informaton loss and "curse of dimensionality" induced by data unfolding. The second one is that it solves the uneven-length problem in a "natural" way without using batch trajectory synchronization, which prevents distortin data and fault patterns and guarantees higher modeling and monitoring precision. An online batch process monitoring method is then developed by integrating GTucker2 with the removing data window techniques Three monitoring statistics named Q R-2, and T-2 statistics are constructed for fault detection and diagnosis. The effectiveness and advantages of the GTucker2-based monitoring method are illustrated by two case studies in a benchmark fed-batch penicillin fermentation process.