Ultrasonic-magnetorheological compound finishing (UMC finishing) is a new technique for the ultraprecision machining of aspheric surfaces, especially for the ultraprecision machining of small-radiused concave surfaces and freeform surfaces. In this article, an UMC finishing equipment with five axes, four of which perform linkage movement, was developed. According to characteristic of UMC finishing, NC interpolation algorithm for rotary symmetric aspheric based on this equipment was researched. The derivation process and computer simulation result of the algorithm were also presented. The interpolation error of this algorithm was analyzed and the calculation formula was also proposed. According to the result of analysis, the precision of the interpolation algorithm is high and the algorithm is very useful. A great number of polishing experiments prove that high quality aspheric surface can be machined using this numerical interpolation algorithm. The profile accuracy of 58.32 nm and surface roughness Ra of 0.746 nm can be obtained stably.