The invention discloses a machining method of a non-rotation tool numerical control machining complex curved surface. According to the machining method, a discrete algorithm of the effective feature lines of the non-rotation tool numerical control machining complex curved surface is utilized to obtain a tool trajectory of a maximum line width. The discrete algorithm includes the following steps that: a reasonable tool curved surface is obtained, and a driving tool motion form is obtained; the motion equation of a tool and workpiece connection point and the motion equation of the rotation of the tool curved surface around the connection point are established; a corresponding transformation equation of the transformation of the original parameter space of the tool curved surface to any position coordinate system is established; the feature line at any position of the tool curved surface is solved, a tool working surface is obtained; longitude lines or latitude lines are obtained; and shortest distance points between the plurality of longitude lines or latitude lines and the workpiece curved surface are solved and are connected together, so that effective feature line segments are obtained; and parameters are adjusted, so that a tool trajectory of a maximum line width is obtained. With the machining method of the invention adopted, an effective solution can be provided for machining a complex curved surface.