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According to the method of principal component analysis(PCA)and locality preserving projections(LPP)can respectly retain the global information and local information of the data set in the process of reducing dimension,a novel method named local and global structure preserving projections and bayes (LGSPP-Bayes) was proposed. Firstly,projecting the original data under normal operating conditions onto a low dimensional feature space to get a data transformation matrix from high dimension to low dimension; Then designing bayesian classifier for fault detection; Finally when a fault was detected,identifying which kind of the fault is by calculating bayesian classification functions. Case applying to Tennessee Eastman process illustrates the new method is better than other methods in the detection of fault. Besides,it is also a good way to identify fault types. 