This work reports new photometric results of eclipsing cataclysmic variable V617 Sagittarii (V617 Sgr). We analyzed the orbital period change of V617 Sgr by employing three new (since 2010) CCD eclipse timings along with all the available data from the literature. It was found that the orbital period of V617 Sgr undergoes an obvious long-term increase, which confirms the result revealed by Steiner et al. (2006). The rate of orbital period increase was calculated to be P = +2.14(0.05) × 10-7 d yr-1. This suggests the lifetime of the secondary star will end in a timescale of 0.97 × 106 yr faster than that predicted previously. In particular, a cyclic variation with a period of 4.5 yr and an amplitude of 2.3 min may appear in the O - C diagram. Dominated by the wind-accretion mechanism, high mass transfer from the low mass secondary to the white dwarf is expected to continue in the V Sge-type star V617 Sgr during its long-term evolution. The mass transfer rate |Mtr| was estimated to be in the range of about 2.2 × 10-7 to 5.2 × 10-7 M⊙ yr-1. Accordingly, the already massive (≥ 1.2 M⊙) white dwarf primary will process stable nuclear burning, accrete a fraction of the mass from its companion to reach the standard Chandrasekhar mass limit (≃ 1.38 M⊙), and ultimately produce a type Ia supernova (SN Ia) within about 4-8 × 105 yr or earlier.