New complete light curves in B, V, R-C, and I-C bands for the short-period eclipsing binary V0627 Hya (period shorter than 0.22 d) are presented. From the longer wavelength to the shorter one, the amplitudes of the light variation become larger. The different height of the successive maxima in each band's light curve could be seen clearly. We analyzed those multi-wavelength light curves using the Wilson-Devinney code and derived the photometric solutions of V0627 Hya for the first time. It is found that V0627 Hya is a W-type shallow-contact binary. Combined with the GAIA parallax, the absolute parameters of this system are obtained: M-1 = 0.31 M-circle dot, M-2 = 0.64 M-circle dot, R-1 = 0.50 R-circle dot, R-2 = 0.69 R-circle dot, L-1 = 0.06 L-circle dot, L-2 = 0.08 L-circle dot. Thus, V0627 Hya is a new member of the red dwarf contact binary class. The asymmetry in the light curves could be explained by the spot model due to the magnetic activity of its late-type component. The amplitude differences in the different bands' light curves imply the existence of a cool third body, which is supported by the third light contribution in the photometric solutions. The third body in this system may play an important role in its formation and evolution by removing the angular momentum. More red dwarf contact binaries need to be found and studied, since they are rare and not enough is known to reveal their mysteries at present.