A novel data projection algorithm named tensor global-local preserving projections (TGLPP) is proposed for three-way data arrays. TGLPP is able to preserve global and local structures of data simultaneously. TGLPP builds a unified framework for global structure preserving and local structure preserving. Tensor principal component analysis (TPCA) and tensor locality preserving projections (TLPP) are unified in the TGLPP framework. They are proved to be two limiting cases of TGLPP. A batch process monitoring method is then developed on the basis of TGLPP. The SPD statistic and R-2 statistic are used for fault detection. The contribution plot is applied for fault identification. Two case studies are carried out to validate the efficiency of TGLPP-based monitoring method.