Industrial processes are characterized by large amounts of nonlinear and noisy data, which pose a critical challenge to the accuracy and rapidity of fault detection. In this paper, an industrial process fault monitoring method based on kernel robust non-negative matrix factorization is proposed. This method uses the kernel technique to map the nonlinear data to high-dimensional linear space, where the local features of the sample will be extracted by the non-negative matrix factorization (NMF) method. However, noise signals will inevitably be mixed. Therefore, a sparse error matrix is introduced to isolate fault and noise information. Finally, a new monitoring statistics and a fault detection framework are constructed. On the TE platform, the algorithm proposed in this paper is compared with kernel principal component analysis and kernel NMF methods in nonlinear experiments and robustness experiments through two performance indicators: fault detection rate and fault delay. The results prove the effectiveness of the algorithm in this paper.