Stretch lengths of pure gold mono-atomic wires have been studied recently with an electrochemical scanning tunneling microscope (STM). Here, we will report a study of stretch lengths of gold mono-atomic wires with and without 1,6-hexanedithiol (HDT) using the STM break-junction method. First, the stretch length was measured as a function of electrode potentials of a bare Au(111) substrate and a gold STM tip in a 0.1 M NaClO4 aqueous solution. Second, a self-assembled monolayer (SAM) was fabricated on an Au(111) substrate by dipping the substrate into a 1 mM HDT ethanol solution. At last, we measured the stretch length of gold mono-atomic wires on a substrate covered with the SAM in place of the bare Au(111) substrate. We compared the electrode potential dependence of the stretch lengths of gold mono-atomic wires covered with and without HDT. We will discuss the effect of the electrode potential on the stretch lengths by taking account of electrocapillarity of gold mono-atomic wires.