The invention belongs to the multi-axis numerical control machining technical field and relates to an equivalent plane cross-coupling control method, in particular, an equivalent plane-based three-axis cross-coupling control method used for improving the contour tracking control precision of a three-axis numerical control system. According to the method, an approximate foot of perpendicular from an actual cutter location point to an ideal contour is searched through tangential retroduction and Newton' method, so that an equivalent plane that passes through the tangent line of a curve at the approximate foot of perpendicular and the actual cutter location point is established; three-dimensional contour error vectors are decoupled into two-dimensional contour error scalars in the equivalentplane; PID control is performed on contour error scalars having symbols in the equivalent plane; two-axis control quantities are in the equivalent plane are coupled into actual space three-axis control quantities; and therefore, three-axis contour tracking accuracy can be improved. With the method adopted, the flexibility of the design of a contour controller can be improved; a three-dimensional contour error control problem is equivalent to a two-axis contour error control problem; equivalent control over three-dimensional contour tracking errors can be realized by using a two-dimensional contour controller.