The conductance of a single 1,4-diisocyanatobenzene molecule sandwiched between twosingle-walled carbon nanotube (SWCNT) electrodes are studied using a fully self-consistentab initio approach which combines nonequilibrium Green's function formalism with densityfunctional theory calculations. Several metallic zigzag and armchair SWCNTs with differentdiameters are used as electrodes; dangling bonds at their open ends are terminated with hydrogenatoms. Within the energy range of a few eV of the Fermi energy, all the SWCNT electrodes couplestrongly only with the frontier molecular orbitals that are related to nonlocal π bonds. Although thechirality of SWCNT electrodes has significant influences on this coupling and thus the molecularconductance, the diameter of electrodes, the distance, and the torsion angle between electrodes haveonly minor influences on the conductance, showing the advantage of using SWCNTs as theelectrodes for molecular electronic devices.