Using the density-functional theory within the full-potential linear augmented plane wave method, we have calculated the influence of the mercury vacancy on the bonding mechanism and the relaxation effects in the Hg050.5Cd 050.5Te (MCT) alloy. The bonding charge density and charge transf er gave the explanation for the relaxation results. The results of density of st ates revealed that the re-coupling of the dangling bond of the nearest neighbor (NN) of the vacancy make the NN Te 5s state energy level shift up. The reasons for the energy level shift were discussed with the Te s-state bonding charge density. The results of the partial density of state at the band edge reveal that the mercury vacancy will narrow the band gap of the MCT materials.