The electron transport properties of the single molecular junctions composed of isomers of 4,4-(ethene-1,2-diyl) dibenzoic acid and two gold electrodes are investigated systematically using elastic scattering Green's function method. The conductance characteristics are quite different for the two isomers which can be used to construct molecular switch. Our study shows that the molecules are chemically adsorbed on the gold surface by the terminal carboxyl group. Each molecular junction has three different stable conductances, which correspond to the different contact structures between the molecules and electrodes. The different conductances result mainly from the variation of the electronic structures, caused by the interaction between the molecules and the electrodes. Our theoretical simulation is consistent with the experimental measurement.