This paper presents a semi-supervised kernel-based fuzzy c-means algorithm called S2KFCM by introducing semi-supervised learning technique and the kernel method simultaneously into conventional fuzzy clustering algorithm. Through using labeled and unlabeled data together, S2KFCM can be applied to both clustering and classification tasks. However, only the latter is concerned in this paper. Experimental results show that S2KFCM can improve classification accuracy significantly, compared with conventional classifiers trained with a small number of labeled data only. Also, it outperforms a similar approach S2FCM.