V0405 Dra is a W UMa-type binary star. Basing on the TESS data, we have conducted an orbital period study and performed a light curve analysis for the system. The orbital period study reveals that the $O-C$ curve for V0405 Dra exhibits secular decrease at an extremely high rate of $dP/dt = -2.71 \times 10^{-6} day\cdot year^{-1}$, along with periodic variations characterized by an amplitude of $A_3 = 0.0032$ days and a period of $P_3 = 1.413 $ years. The orbital periodic change is possibly due to the light-travel time effect resulting from an additional third body in the system, for which we estimate a minimum mass of $M_3 = 0.77 M_{\odot}$. By employing the \add{2013 version of the} Wilson-Devinney (W-D \add{2013}) method to synthesize light curve, we derived photometric solutions indicating that V0405 Dra is a new deep ($f = 68.7\%$)and low-mass ratio ($q =0.175$) contact binary. The fast decrease in its orbital period is likely caused by mass transfer from the more massive primary star to the less massive secondary star, or due to angular momentum loss, which have been elaborated upon in the last section. With further mass transfer and loss of angular momentum, the binary will gradually evolve into a tighter contact configuration, eventually leading to a merge into a single star, following the evolutionary paths suggested for such deep and low mass ratio contact binaries.