A new grid-based method is proposed for predicting the behaviour of colour printers. The method takes into account the varying density of dots as well as the light diffusion in the paper by defining at different intensity levels different colorimetric values for the printed ink as well as for the paper white. Since the model integrates both the varying density of partly overlapping ink dots and the light diffusion in the underlying substrate, the obtained predictions are more accurate than those obtained with surface based colour prediction methods described in the literature.