Capillary tubes used in medical equipment are desired to have higher form accuracy and higher inner surface integrity as the improvement of the medical equipment rapidly progresses. In terms of the surface integrity, the capillary tubes need to have smoother inner surfaces to prevent impurities from contaminating. To reply to the demand, this research proposes a new magnetic field assisted micro-machining process. This paper presents the finishing principle and the experimental setup developed to demonstrate the principle. As a first trial, the machining characteristics were examined by the finishing experiments of plane surfaces. The experiments demonstrated the effects of the abrasive size on the changes in the surface roughness profiles with machining time, resulting in the feasibility of the process.