The invention belongs to the technical field of numerical control processing and manufacturing, in particular to a cutter shaft interpolation algorithm which can be used for carrying out peripheral milling on a five-axis linkage numerically-controlled machine tool, and effectively controlling a cutter shaft vector in an inclined plane, thus eliminating non-linear error caused by adopting the traditional linear interpolation of a rotating shaft angle. In the algorithm, a new coordinate system is constructed according to the definition and property of the vector; circular interpolation is carried out on the plane at the new coordinate system, so as to obtain a new cutter shaft vector; the new cutter shaft vector is transformed into the cutter shaft vector at the coordinate system of the machine tool; the condition that the cutter point can move along a programming track can be controlled, and the cutter shaft vector is kept on the same plane all the time through the algorithm, and by combining compensation of a (rotation tool center point) RTCP; the algorithm is provided for eliminating the non-linear error in inclined plane processing by peripheral milling, and also can be applied in the peripheral milling of a free-formed surface; and additionally, the algorithm contributes to optimize end-milling processing; thus on one hand, the fluctuation of the cutter point can be prevented, and the processing precision can be improved; and on the other hand, the condition that the cutter can not deviate the effective cutting edge of the cutter is ensured, and abnormal wear and tear of the cutter is reduced, thus the surface quality of a workpiece can be improved.