Hyperboloidal-type normal circular-arc gears (HNCGs) are a latest application of circular-arc tooth profile in the gearing with perpendicular non-intersection axes, and the existing software programs provided by the original equipment manufacturers (OEMs) for specific machine tools cannot yet directly support the manufacture of HNCGs. In this paper, a dimension-driven adaptive programming methodology is proposed to automatically carry out the tool-path planning and generate the G-code file for the form milling of HNCGs on general 5-axis CNC machine tools. Based on the mathematical model of tooth surface, the basic strategy for 5-axis form milling of tooth is presented, an interference-free tool path considering both roughing and finishing operations is planned, and furthermore, the tool-path data is transformed to achieve the machine tool coordinates. To quickly respond to the changes of design and machining parameters, a dimension-driven adaptive programming software package is developed to automatically compute the tool path, conduct the post-processing, and generate the G-codes for 5-axis form milling of HNCGs with different specifications, and example verification is carried out to demonstrate the validity of the proposed method.