As a special order of electronic correlation induced by spatial modulation, the charge density wave (CDW) phenomena in condensed matters attract enormous research interests. Here, using scanning-tunneling microscopy in various temperatures, we observe a new (2×1) CDW phase besides the (√7×√3) CDW phase in epitaxial monolayer 1T-VSe2 film. Combining the variable-temperature angle-resolved photoemission spectroscopic (ARPES) measurements, we discover an anisotropic CDW gap and a two-step transition associated with the different CDW phases, which were observed below 135 K for the (√7×√3) CDW phase and between 135 K to 330 K for the (2×1) CDW phase respectively. The (√7×√3) CDW phase results a full gap, while the (2×1) CDW phase shows highly momentum dependence and results a partial gap structure at the Fermi surface. This two-step transition with anisotropic gap opening and the resulted evolution in ARPES spectra are corroborated by our theoretical calculation based on a phenomenological form for the self-energy containing a two-gap structure. Our findings provide significant information and deep understanding on the CDW phases in monolayer 1T-VSe2 film as a 2D material.