The first four-color light curves of V868 Mon in the $B$ $V$ $R_c$ and $I_c$ bands are presented and analyzed by using the Wilson-Devinney method of the 2013 version. It is discovered that V868 Mon is an A-subtype contact binary (f=$58.9,%$) with a large temperature difference of 916$K$ between the two components. Using the eight new times of light minimum determined by the authors together with those collected from literatures, the authors found that the general trend of the observed-calculate ($O$-$C$) curve shows a upward parabolic variation that corresponds to a long-term increase in the orbital period at a rate of $dP/dt=9.38times{10^{-7}}daycdot year^{-1}$. The continuous increase may be caused by a mass transfer from the less massive component to the more massive one.