We present a method to precisely determine the hyperfine structure constants of the rubidium $5{\mathrm{D}}_{5/2}$ and $7{\mathrm{S}}_{1/2}$ states in a cascade atomic system. The probe laser is coupled to the $5{\mathrm{S}}_{1/2}\to 5{\mathrm{P}}_{3/2}$ hyperfine transition, while the coupling laser is scanned over the $5{\mathrm{P}}_{3/2}\to 5{\mathrm{D}}_{5/2}(7{\mathrm{S}}_{1/2})$ 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.