In this paper we present a generalised Wishart classifier derived from a non-Gaussian model for polarimetric synthetic aperture radar (POLSAR) data. Our starting point is to demonstrate that the scale mixture of Gaussian (SMoG) distribution model is suitable for modelling POLSAR data. We show that the distribution of the sample covariance matrix for the SMoG model is given as a generalisation of the Wishart distribution, and present this expression in integral form. We then derive the closed form solution for one particular SMoG distribution, known as the multivariate K-distribution. Based on this new distribution, termed the K-Wishart distribution, we propose a Bayesian classification scheme, which can be used in both supervised and unsupervised mode. Modelling and classification is tested on airborne EMISAR data.