Take the Quadrangular-Pyramid-Shaped Fiber Endface(QPSFE) and the Conical-Wedge-Shaped Fiber Endface(CWSFE) for example, the present procedure of grinding asymmetric optical fiber endface demands three to four steps. These steps take time and are lack of repeatability and high yield. Aim at the shortcomings, this study develops a set of mechanism to attach to the original optical fiber grinding machine. The mechanism makes the normal pressure between the endface and the grinding plate change periodically to modify the removing rate of the material, thus enables the clipped flat endface of the optical fiber be ground into an elliptic-cone-shaped in a single grinding step, and then becomes a lens after its tip being fused by the arc. This mechanism reduces the fabricating time and cost, and consequently improve the economic benefits as well by simplifying the complicated manufacturing processes that represented before. Besides, for its single-step grinding characteristic, the offset between the center of the fiber and the elliptic-cone can thus be slashed to promote the yield. This study reviews the anterior references, including the papers and the patents, to begin, and then proposes the current means to compare with. Its contents involve the development of the forming principle, which proposes how the variation of the normal pressure takes influence on the removing rate of the material, and the required mechanism for the design procedure. The mechanism, the research result, and those needed to be ameliorated will be demonstrated in the conclusion and discussion part, so as to offer the investigating direction in the future.