Multinomial logistic regression is a well known multiclass classification method in the field of statistical learning. More recently, the development of sparse multinomial logistic regression model has found application in microarray classification, where explicit identification of the most informative observations is of value. In this paper, we propose a sparse multinomial kernel logistic regression model, in which the sparsity arises from the use of a Laplacian prior and a fast exact algorithm is derived by employing a bound optimization approach. Experimental results are then presented to indicate the performance of the proposed procedure.