New light curves in B, V, R, and I bands for the B-type contact binary V593 Cen were obtained, and another V-band light curve was collected from All Sky Automated Survey data. We analyzed these two sets of light curves using the Wilson-Devinney code. It was found that V593 Cen is a deep-contact binary with a fill-out factor of more than 45%. The mass ratio, derived to be nearly one from light curves, indicates that this system contains two twin components. Together with the higher temperature of the less-massive component, it is inferred that the system has just passed the mass-reversal stage during the mass-transfer evolution. Therefore, at present it has the shortest period and deepest-contact configuration. By analyzing all available eclipse times, it is found that the O - C curve of V593 Cen shows a cyclic variation with a period of 50.9 yr. This can be explained as the light-travel time effect via the presence of a third body. The mass of the third body is derived to be larger than 4.3 (+/- 0.3) M-circle dot, and it should contribute to the total light of the system. However, no third light is detected during the photometric analyses. This indicates that it may be a black hole candidate orbiting the central mass-transferring binary in a triple system. During the evolution of this hierarchical triple-star system, the "eccentric Kozai-Lidov" mechanism may play a major role in the formation of the inner contact binary. This system seems a perfect candidate to be one of "merged" systems mentioned by Naoz & Fabrycky.