We report a grinding technique called the "arc envelope grinding method (AEGM)" and its grinding tests. In conventional form-generation grinding, loading and dulling of a diamond wheel can easily occur, which decrease both the machining accuracy and the wheel life, since the same part of the wheel is always used. In AEGM, a diamond wheel with a round profile is used and the workpiece profile is an envelope of a family of arcs. Since the grinding point is changed along the wheel profile with every grinding pass, the entire wheel width can be used and the wheel life is prolonged. In this study, arc truing accuracy, wheel design, surface roughness and form accuracy of the ground workpiece are investigated. Using the AEGM, nonaxisymmetric aspheric mirrors of silicon carbide were successfully ground. The form error after the first grinding (without any compensation) was less than ±0.8μm, and the roughness was R_max=0.2μm.