The invention relates to the technical field of machining, in particular discloses a follow-up turning device and method of a thin-wall curved generatrix revolving part. The device comprises a mould, a pressing structure, a numerical control system and a turning structure. A part to be machined is put on the mould similar to the part to be machined in curve radian, and is pressed and fixed through a tail tightening piece at the rightmost end; both the pressing structure and the turning structure are pressed against the surface of the part to be machined; and the motion trails of the pressing structure and the turning structure are controlled through the numerical control system, wherein the numerical control system sends a numerical control signal, controls a servo system connected with the turning structure, and drives the turning structure to machine the part to be machined. In the device and the method, a pressing wheel of the pressing structure forms a stable pressing area around a pressing point, and a turning point is positioned in the stable pressing area, so that the part with better wall thickness uniformity can be turned by selecting a pressing wheel with the proper fillet radius, a proper locus of the pressing wheel, a turning tool with the proper fillet radius, a proper locus of the turning tool and a proper turning amount.