The invention pertains to a combustion grate assembly for a combustion plant, the grate assembly comprising a cascade of inclined grates, the grates being mounted with a step between the grates so that fuel is able to move from one grate in the cascade down to the next grate in the cascade under the influence of the force of gravity, and wherein each grate is connected to a vibrating system for vibrating the grates and thereby advancing the fuel from a fuel inlet zone on the first grate in the cascade to a bottom ash discharge zone on the last grate in the cascade. Each grate may be connected to an individual vibrating system for vibrating the grates independently of each other. The invention also pertains to a method of combusting biomass or other fuel.