The conductance of a molecular device is sensitive to the contact geometry between the molecules and the probing electrodes. Combining the density functional theory calculations (DFT) for molecular electronic structure with a non-equilibrium Green’s function (NEGF) method for electron transport, we calculate the molecular conductance of carbon dimer connected between Au leads through two different anchoring atoms  Se and Te. The current-voltage characteristics and transmission spectra of two systems are studied. The results exhibit that, depending on the anchoring groups and the subsequent different metal-molecule chemical bonds, the current varies over more than four times of magnitude under the same bias. Furthermore, the system exhibits negative differential resistance (NDR) effect, when anchored with Te atom. This emphasizes  the great importance of the anchoring groups in molecular devices.