Modern chemical processes are usually characterized by their large scale and nonlinearity, and the monitoring of such processes is imperative. This paper proposes fault-relevant kernel principal component (KPC) subspace construction integrated with a Bayesian inference method to achieve efficient monitoring of nonlinear chemical processes. First, KPC analysis is performed to deal with process nonlinearity and generate a KPC feature space. Second, a fault-relevant KPC (FRKPC) subspace is constructed for each fault through KPC selection using a stochastic optimization algorithm. Then, a new process measurement is examined in each FRKPC subspace, and the monitoring results from all subspaces are fused in a comprehensive index through Bayesian inference to provide an intuitive indication of the process status. The FRKPC subspace construction method reduces redundancy in monitoring and therefore improves monitoring performance significantly. The proposed method is applied to a numerical example and the Tennessee Eastman benchmark process. These monitoring results demonstrate the efficiency of the proposed method.