In modern complex industrial processes, mode changes cause unplanned shutdowns, potentially shortening the lifespan of key equipment and incurring significant maintenance costs. To avoid this problem, a method that can detect the fault of equipment operating in various modes is required. Therefore, we propose a novel fault detection method that uses the k-nearest neighbor normalization-based weight local outlier factor (WLOF). The proposed method performs local normalization using neighbors to consider possible mode changes in the normal data and WLOF is used for fault detection. In contrast to statistical methods, such as principal component analysis (PCA) and independent component analysis (ICA), the local outlier factor (LOF) uses the density of neighbors. However, because LOF is significantly affected by the distance between its neighbors, the weight is multiplied proportionally to the distance between each neighbor to improve the fault detection performance of the LOF. The efficiency of the proposed method was evaluated using a multimode numerical case and a circulating fluidized bed boiler. The experimental results show that the proposed method outperforms conventional PCA, kernel PCA (KPCA), k-nearest neighbor (kNN), and LOF. In particular, the proposed method improved the detection accuracy by 20% compared with conventional methods. Therefore, the proposed method can be applied to a real process operating in multiple modes.