A cylinder interpolation system for machining a cylindrical surface of a cylindrical work. Tool diameter correction means (104) calculates an offset vector of a tool diameter with respect to a machining shape instructed on imaginary orthogonal coordinates and determines the center passage of a tool. Interpolation means (107) interpolates this center passage and outputs an interpolation pulse (PCyi) of an imaginary linear axis and an interpolation pulse (Pzi) of a cylinder axis. To inversely convert the imaginary orthogonal coordinates to the cylinder coordinates, the interpolation pulse (PCyi) is converted to a pulse (PCi) for rotating the axis of rotation by pulse conversion means (108). On the other hand, means (105) and means (109) calculate a corrective component (Vcy) at the beginning of a block and a synchronous corrective component (ΔVcy), respectively. These corrective components (Vcy, ΔVcy) are interpolated by means (106) and means (110) and added to the pulse (PCi) for rotating the axis of rotation. In this way, the tool cutting surface is controlled so that it exists always immediately above the center axis of rotation and the machined surface is vertical to the cylindrical surface of the work.