Complex chemical process has the characteristics of nonlinear and multi-mode, so the on-line monitoring is of great significance to the system security. Based on a large number of industrial process data with complex distribution, this paper proposes a locally linear embedded (LLE) compound statistic fault detection method based on Gaussian weighted adaptive selection k-nearest neighbor. First, the K nearest neighbors (KNN) in the LLE algorithm are selected adaptively by the Gaussian weighted KNN algorithm. Then, the low dimensional sub-epidemic of high dimensional data is extracted by the LLE algorithm, and the mapping matrix from high-dimensional data to low-dimensional data is obtained by local linear regression. In addition, a compound statistic is proposed to complement the T2 and SPE statistics to ensure a satisfying detection effect. Finally, the simulation of Tennessean-Eastman (TE) chemical data is carried out and compared with the classical detection method to verify the effectiveness of the proposed algorithm.