Complex chemical processes often have multiple operating modes to meet changes in production conditions. At the same time, the within-mode process data usually follow a complex combination of Gaussian and non-Gaussian distributions. The multimodality and the within-mode distribution uncertainty in multimode operating data make conventional multivariate statistical process monitoring (MSPM) methods unsuitable for practical complex processes. In this work, a novel method called neighborhood standardized local outlier factor (NSLOF) method is proposed. The local outlier factor of each sample, which means the degree of being an outlier, is used as a monitoring statistic. A new normalized Euclidean distance based on the local neighborhood standardization strategy is employed during the calculation of the monitoring index. Then, a contribution-based fault identification method is developed. Instead of building multiple monitoring models for complex chemical processes with different operating conditions, the proposed NSLOF method builds only one global model to monitor a multimode process without needing a priori process knowledge. Finally, the validity and effectiveness of the NSLOF approach are illustrated through a numerical example and the Tennessee Eastman process.