Structural and electronic detail at the metal molecule interface has a significant impact on the charge transport across the molecular junctions, but its precise understanding and control still remain elusive. On the single-molecule scale, the metal-molecule interface structures and relevant charge transport properties are subject to fluctuation, which contain the fundamental science of single-molecule transport and implication for manipulability of the transport properties in electronic devices. Here, we present a comprehensive approach to investigate the fluctuation in the metal-molecule interface in single-molecule junctions, based on current-voltage (I-V) measurements in combination with first-principles simulation. Contrary to conventional molecular conductance studies, this I-V approach provides a correlated statistical description of both the degree of electronic coupling across the metal molecule interface and the molecular orbital energy level. This statistical approach was employed to study fluctuation in single-molecule junctions of 1,4-butanediamine (DAB), pyrazine (PY), 4,4'-bipyridine (BPY), and fullerene (C-60). We demonstrate that molecular-dependent fluctuation of (sigma-, pi-, and pi-plane-type interfaces can be captured by analyzing the molecular orbital (MO) energy level under mechanical perturbation. While the MO level of DAB with the sigma-type interface shows weak distance dependence and fluctuation, the MO level of PY, BPY, and C-60 features unique distance dependence and molecular-dependent fluctuation against the mechanical perturbation. The MO level of PY and BPY with the sigma+pi-type interface increases with the increase in the stretch distance. In contrast, the MO level of C-60 with the pi-plane-type interface decreases with the increase in the stretching perturbation. This study provides an approach to resolve the structural and electronic fluctuation in the single molecule junctions and insight into the molecular-dependent fluctuation in the junctions.