Kernel principal component analysis (KPCA) has been widely applied to the nonlinear process fault diagnosis field. However, it often does not perform well in the case of incipient faults because of the omission of local data information. To overcome this problem, one enhanced KPCA method, called the two-step localized KPCA (TSLKPCA), is proposed for incipient fault diagnosis in this work The two steps are designed to mine the local data information better. At the first step, the KPCA optimization objective is modified by integrating the local structure preservation so that the extracted kernel components preserve the global and local data structure information simultaneously. At the second step, for the extracted kernel components, the local probability information is further mined by the Kullback Leibler divergence (KLD), which measures the variations of the kernel components' probability distributions. On the basis of these two steps, the original kernel components are transformed into the KLD components, and the corresponding model is developed for incipient fault detection. To isolate the faulty variables, the contribution plot is constructed based on the mutual information between the measured variables and the KLD components obtained by TSLKPCA. Finally, two simulations of a numerical example and the continuous stirred tank reactor (CSTR) control system show that the proposed method has good incipient fault detection and diagnostic performance.