In this paper, single molecular junctions of Para-phthalic acid and Meta-phthalic acid with Au electrodes were studied by STM break junction approach. Conductance values of 10-3.55 G0 and 10-3.70 G0 were found for Para-phthalic acid and Meta-phthalic acid, respectively. The conductance order between Para-phthalic acid and Meta-phthalic acid with Au is different from that with Cu, which can be contributed to the different coupling between molecules and electrodes; different through-space interaction is proposed for such phenomenon between Cu and Au electrodes. Furthermore, the breaking off distances can reflect the length of molecules. The current work presents the important role of electrode in single molecular junctions with different position anchoring groups.