This invention relates to a control apparatus for numerical control in a cutting machine having a turret which can be rotated to arbitrary positions, and characterized by including means for obtaining turret axis data (ΔX, ΔZ) from reference offset values (X0, Z0) corresponding to a length from a cutting edge to a turret axis B, turret angle data α, and cutting edge data (m, n), and moving the turret on the basis of these turret axis data (ΔX, ΔZ) to perform a cutting.