OO Dra is a short-period Algol system with a δ Sct-like pulsator. We obtained time-series spectra between 2016 February and May to derive the fundamental parameters of the binary star and to study its evolutionary scenario. The radial velocity (RV) curves for both components were presented, and the effective temperature of the hotter and more massive primary was determined to be T eff,1 = 8260 ± 210 K by comparing the disentangling spectrum and the Kurucz models. Our RV measurements were solved with the BV light curves of Zhang et al. using the Wilson-Devinney binary code. The absolute dimensions of each component are determined as follows: M 1 = 2.03 ± 0.06 M⊙, M 2 = 0.19 ± 0.01 M⊙, R 1 = 2.08 ± 0.03 R⊙, R 2 = 1.20 ± 0.02 R⊙, L 1 = 18 ± 2 L⊙, and L 2 = 2.0 ± 0.2 L⊙. Comparison with stellar evolution models indicated that the primary star resides inside the δ Sct instability strip on the main sequence, while the cool secondary component is noticeably overluminous and oversized. We demonstrated that OO Dra is an oscillating post-mass transfer R CMa-type binary; the originally more massive star became the low-mass secondary component through mass loss caused by stellar wind and mass transfer, and the gainer became the pulsating primary as the result of mass accretion. The R CMa stars, such as OO Dra, are thought to have formed by non-conservative binary evolution and ultimately to evolve into EL CVn stars.