A cutter head, for a non-rotary power lawn mower, having a multiple-blade, multiple levels of blades assembly. The cutter head includes a stationary assembly in the form of a plurality of fingers arranged in several levels that cooperate with a continuous plurality of blades moved by a blade-carrying assembly. The fingers preferably extend parallel to the lawn mower's direction of motion in order to catch the grass and set it up for cutting. The blade-carrying assembly is preferably a chain conveyed around a pair of sprockets that carry the plurality of blades. These blades are arranged in several levels and interleave several levels of fingers. The grass entering the spacing between the fingers is sheared at each level of the stationary assembly by movement of the blades across the fingers. The cut grass is directed to the rear area of the cutter head, where it falls below the cutter head as mulch.