This paper gives a mathematical model for spur gears with asymmetric involute teeth based on the gear theory and generating mechanism. The equations of designed profile of rack cutter with asymmetric teeth, the principle of coordinate transformation, the theory of differential geometry, and the theory of gearing are applied. Trochoidal envelope traced by cutter during generating process is also investigated. Computer graphs of asymmetric involute spur gears are presented based on the given model, and also generation simulation is illustrated. The results of this research should be helpful in the design and manufacture of asymmetric gears.