A new type of gear pair, the curve-face gear pair, composed of a curve-face gear and a non-circular gear with mutual engagement, was proposed to achieve variable ratio transmission of motion and power between the intersecting axes. Geometric error detection is required to evaluate the grade of the manufactured gears. Due to the complexity of the curve-face gear, direct detection has been conducted in a very limited way. In this article, a measurement method aimed at curve-face gear pair artifacts is presented based on the computer numerical control gear measuring center. By comparing the measured coordinate data of the surface points with the corresponding theoretical data, various errors such as tooth profile error and pitch deviation can be obtained, and accuracy grades are evaluated with reference to accuracy standards for cylindrical gear and bevel gear. The developed method is simple and robust without requiring a special measuring device; hence, it can be applied for the industrial practice as a means for measuring the tooth profile and pitch deviations which cannot be measured by conventional methods.