New CCD BVR light curves of BD And are presented. Our light curves with nearly equal depths for both primary and secondary eclipses show well-defined photometric waves outside eclipse for all of BVR bandpasses. The orbital period is greatly revised as $0.^d92580519$ which is twice longer than that known previously. Sixteen timings from our observations and thirteen ones from the SuperWASP measurements were calculated. All available timings over 76 years, including ours, were analyzed to figure out the dynamical behavior of the system. It was found that the recent CCD O-C residuals varied in a cyclical way with a period of $9.^y18$ and a semi-amplitude of $0.^d0046$. The secondary period of $9.^y18$ is the most shortest one among those which have been ever found in the short period RS CVn binary stars. The periodic variation most likely arises from the light-travel time effect due to a low-mass ($m_3{sim}0.88;M_{odot}$) tertiary companion moving in an orbit with an large eccentricity ($e_3$=0.70) and a low inclination ($i_3{sim}28^{circ}$). The Applegate mechanism could not operate properly in both components because the model parameters require too much large luminosity changes of ${Delta}L/L_{p,s}$ > 10. The new light curves were synthesized using the 2003 version of Wilson-Divinney code. It was found useful to model two huge spots on the surface of the hotter star and a third-light in order to minimize the residuals from the observations. Astronomical basic parameters were deduced from our photometric solution.