Automated classification of sea-ice types in Synthetic Aperture Radar (SAR) imagery is compli- cated by the class-dependent decrease of backscatter intensity with Incidence Angle (IA). In the log-domain, this decrease is approximately linear over the typical range of space-borne SAR instruments. A global correction does not consider that different surface types show different rates of decrease in backscatter intensity. Here, we introduce a supervised classification algorithm that directly incorporates the surface-type dependent effect of IA. We replace the constant mean vector of a Gaussian probability density function in a Bayesian classifier with a linearly variable mean. During training, the classifier first retrieves the slope and intercept of the linear function describing the mean value and then calculates the covariance matrix as the mean squared devi- ation relative to this function. The IA dependence is no longer treated as an image property but as a class property. Based on training and validation data selected from overlapping SAR and optical images, we evaluate the proposed method in several case studies and compare to other classifi- cation algorithms for which a global IA correction is applied during pre-processing. Our results show that the inclusion of the per-class IA sensitivity can significantly improve the performance of the classifier.