Abstract: The industrial process has the characteristics of high complexity and dynamics. During feature extraction, the utilization of time-delay factor for expanding the matrix of time-series data can overcome the self-correlation and cross-correlation problem of field variables. When a feature extraction algorithm is utilized to deal with the extension data of three-order tensor form, it usually needs to vectorize the three-order tensor in a certain direction, which will destroy the intrinsic two-dimensional structure information in the original data. Aiming at the above shortcoming, this paper proposes a tensor-temporal extension locality preserving projection (T-TELPP) algorithm based on tensor space. First, locality preserving projection (LPP) algorithm is modified to obtain the temporal extension locality preserving projection (TELPP) algorithm so that the Euclidean neighbors and the temporal neighbor information can be fully extracted. And then, the TELPP algorithm is extended to tensor space for obtaining the T-TELPP algorithm. A key feature of T-TELPP algorithm is that it projects dynamic extended data into feature space and residual space and establishes T² and SPE statistics, respectively, to realize the process monitoring. Finally, the T-TELPP-based monitoring method is applied in the dynamic chemical process of Tennessee Eastman (TE), which verifies the effectiveness and superiority of the T-TELPP fault detection algorithm in dynamic process monitoring, compared with principal component analysis (PCA), dynamic PCA (DPCA) and dynamic locality preserving projections (DLPP).