We investigate the structure of nonionic fluorosurfactant zonyl FSN self-assembled monolayers on Au(111) and Au(100) in 0.05 M H2SO4 as a function of the electrode potential by electrochemical scanning tunneling microscopy (ECSTM). On Au(111), a (3(1/2) x 3(1/2))R30 degrees arrangement of the FSN SAMs is observed, which remains unchanged in the potential range where the redox reaction of FSN molecules does not occur. On Au(100), some parallel corrugations of the FSN SAMs are observed, which originate from the smaller distance and the repulsive interaction between FSN molecules to make the FSN molecules deviate from the bridging sites, and ECSTM reveals a potential-induced structural transition of the FSN SAMs. The experimental observations are rationalized by the effect of the intermolecular interaction. The smaller distance between molecules on Au(100) results in the repulsive force, which increases the probability of structural change induced by external factors (i.e., the electrode potential). The appropriate distance and interactions of FSN molecules account for the stable structure of FSN SAMs on Au(111). Surface crystallography may influence the intermolecular interaction through changing the molecular arrangements of the SAMs. The results benefit the molecular-scale understanding of the behavior of the FSN SAMs under electrochemical potential control.