In this paper, a fault detection method based on generalized correntropy principal component analysis(PCA) is proposed to deal with the problem that actual chemical processes are affected by non-gaussian disturbances to varying degrees. First, traditional PCA algorithm is briefly reviewed. Then, from the perspective of reconstruction error, by considering the non-gaussian nature of process, the mean square error is not enough to describe its random characteristics. In this paper, the generalized correntropy criterion is adopted to construct the PCA model. Then, the kernel density estimation method is used to determine the control limit of the fault detection index. Finally, the proposed method is applied to the fault detection of Tenenson-Eastman process, and compared with the traditional PCA-based fault detection method and the kernel PCA-based fault detection method. It can be seen from the 21 fault detection results of Tenenson-Eastman process that the generalized correntropy PCA proposed in this paper has a good performance in dealing with the fault detection of non-gaussian systems, that is, it has a low false alarm rate and a low missing alarm rate.