A measurement method for mapping the reflectivity distribution of curved high-reflectivity mirrors based on optical feedback cavity ring-down (OF-CRD) technique is introduced. The setup consists of a high-stability folded optical cavity and a high-precision positioning system with 5 degrees of freedom (DOF). By mathematical modeling, we established a universal mathematical relationship between the curved surface described by mathematical formula and the required adjustment for sample positioning, enabling dynamic five-dimensional compensation for optical elements with varying curvatures, apertures, and surface profiles. Through high-precision automated scanning strategy, the high-reflectivity distributions of samples with different surface profiles, apertures, and curvature diameters are obtained, this measurement is achieved by two-dimensionally raster-scanning while compensating for the other three dimensions (depth, pitch, and yaw) of the samples using a control program to ensure strict normal alignment between the probe beam and local surface throughout the measurement process. A reflectivity measurement repeatability error at the part-per-million (ppm) level is experimentally achieved. Good agreement is observed between the CRD-measured reflectivity profile and the grayscale image obtained by a laser confocal microscopy. Compared with the reflectivity values obtained by manual high-precision alignment, both reflectivity distributions obtained via automatic and manual alignments are consistent, demonstrating the reliability of the reflectivity distribution obtained with the experimental apparatus.