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The layered structure with van der Waals interaction allows flexible stacking configurations creating various heterointerface junctions. This freedom opens new possibilities to tailor the physical properties of TMD materials. Here, we systematically investigate the CDW phases in ML VSe₂ depending on the substrates such as single-layer graphene (SLG) and bi-layer graphene (BLG) via scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES). Interestingly, we find that ML VSe₂ films are less coupled to the SLG substrate compared to that of ML VSe₂/BLG. In addition, ML VSe₂/SLG reveals a clear topographic modulation of 4 × 1 CDW interfering with √3 × 2 and √3 × √7 CDW, while ML VSe₂/BLG shows only one unidirectional modulation of √3 × 2 and √3 × √7 CDW in topography. Furthermore, it is confirmed that the reciprocal vector with 4 × 1 periodicity perfectly satisfies the nesting condition for Fermi surfaces near the M point in ML VSe₂. We propose that the planar projection of the 4 × 4 × 3 CDW in bulk gives rise to the 4 × 1 CDW phase observed in ML VSe₂/SLG. Then, the weakly coupled interface between the VSe₂ film and SLG substrate might facilitate preserving the 4 × 1 CDW phase in ML VSe₂. Our result clarifies the nature of the 4 × 1 CDW in ML VSe₂ system and is a good example demonstrating the essential role of substrates in two-dimensional transition metal dichalcogenides.