Batch production process data usually contains mixture ingredients of the Gaussian and non-Gaussian distribution. Traditional monitoring methods require data to meet the requirements of Gaussian distribution and do not take into account the global and local features for feature extraction. An ICA algorithm can deal with process diagnosis of non-Gaussian distribution but cannot deal with process diagnosis of Gaussian distribution. So a multi-way global neighbourhood preserving embedding, local independent component analysis (MGNPE-LICA) algorithm, is proposed in this paper. Firstly, raw data is divided into Gaussian and non-Gaussian spaces by the D-test. For the Gaussian space, the MGNPE algorithm is used to fully extract local structural features and global structural features of data. For the non-Gaussian space, the MLICA algorithm is used to solve non-Gaussian problems and at the same time reserve global and local information of data. Then the monitoring index of two spaces synthesizes a joint monitoring indicator to monitor the process. The contribution plot method is used to diagnose fault variables after detecting faults. The simulation results of a penicillin fermentation process verified the effectiveness of the proposed algorithm.