Proximity-based fuzzy c-means algorithm (P-FCM), a classical semi-supervised clustering algorithm, concerns with the number of proximity "hints" or constraints that specify an extent to which some pairs of instances are considered similar or. By replacing the fuzzy c-means in P-FCM with a kernel fuzzy c-means, this paper proposes a new semi-supervised clustering algorithm named proximity-based kernel fuzzy c-means (PKFCM), which not only can cluster non-linearly separable data but also can utilize the user inputs about proximity among data to guide the clustering. In addition, PKFCM is able to apply the user inputs to select decent parameters for kernel functions. Simulations on some synthetic data demonstrate the feasibility and advantages of proposed PKFCM. © 2012 IEEE.