A one-dimensional transient model for simulating the conversion of solid biomass fuels in grate boilers is presented. The model considers drying; pyrolysis; and char oxidation; gas flow through the pore space of the bed; conductive, convective, and radiative heat transfer; and shrinkage of the fuel bed. It allows to study the influence of fuel properties and operating parameters on the solid fuel conversion, the resulting grate coverage, and the gas profiles. Experimental results from a 1.2 MW grate boiler at optimum conditions are used to adjust the moving bed velocity in the model. Calculations with increased fuel humidity then result in a prolonged drying time and unburned carbon in the ash. Adopted model runs further reveal that ideal conditions can be recovered either by increasing the excess air, by air pre-heating, or by reducing the boiler capacity. Hence, the model is useful to predict the influence of parameters on the fuel conversion, to evaluate measures for combustion optimization, and to develop control strategies.