We present a method to precisely determine the hyperfine structure constants of the rubidium 5D5/2 and 7S1/2 states in a cascade atomic system. The probe laser is coupled to the 5S1/2→5P3/2 hyperfine transition, while the coupling laser is scanned over the 5P3/2→5D5/2(7S1/2) transition. The high-resolution double-resonance optical pumping spectra are obtained with two counter-propagating laser beams acting on rubidium vapor. The hyperfine splitting structures are accurately measured by an optical frequency ruler based on the acousto-optic modulator, thus, the magnetic dipole hyperfine coupling constant A and quadrupole coupling constant B are determined. It is of great significance for the atomic hyperfine structure and fundamental physics research.