The ultimate goal of this project is to develop an efficient finishing process enabling unskilled operators to finish automatically the complicated micro-curved surface and edge surface of the magnesium alloy. The results achieved in the first phase as described in this paper focus on the basic characteristics of the plane and edge surface finishing and deburring of this alloy by the use of vertical vibration-assisted magnetic abrasive finishing process. It demonstrates that realization of efficient finishing of magnesium alloy is possible by the process. The removal volume per unit time of magnesium alloy is larger than that of other materials such as brass and stainless, that is, high-efficiency finishing could be achieved. Micro-burr of magnesium alloy could be removed easily in a short time by the use of the magnetic abrasive finishing process. Furthermore, deburring efficiency considerably increases with vertical vibration assistance.