Clustering analysis is an important topic in artificial intelligence (AI) and pattern recognition (PR) research. Conventional clustering algorithms, such as the famous Fuzzy C-Means clustering algorithm (FCM) assume that all the attributes are equally relevant to all the clusters. However in most domains, some attributes are irrelevant, and some relevant ones are less important than others for a specific class. In this paper, such imbalance between the attributes is considered and a new weighted fuzzy kernel-clustering algorithm WFKCA is presented. WFKCA performs clustering in high feature space mapped by mercer kernels. Comparing with the conventional hard kernel-clustering algorithm, WFKCA can derive the meaningful prototypes of the clusters. Numerical convergence properties of WFKCA are also discussed. In order to tackle with the incomplete data effectively, we extend WFKCA to WFKCA2, which is demonstrated a useful tool for clustering incomplete data. Finally, we further demonstrate WFKCA is an effective tool for image segmentation with numerical examples.