We present extensive optical photometric and spectroscopic observations of the high-velocity (HV) Type Ia supernova (SN Ia) 2017fgc, covering the phase from $sim$ 12 d before to $sim 389$ d after maximum brightness. SN 2017fgc is similar to normal SNe Ia, with an absolute peak magnitude of $M_{rm max}^{B} approx$ $-19.32 pm 0.13$ mag and a post-peak decline of ${Delta}m_{15}(B)$ = $1.05 pm 0.07$ mag. Its peak bolometric luminosity is derived as $1.32 pm 0.13) times 10^{43} $erg s$^{-1}$, corresponding to a $^{56}$Ni mass of $0.51 pm 0.03 M_{odot}$. The light curves of SN 2017fgc are found to exhibit excess emission in the $UBV$ bands in the early nebular phase and pronounced secondary shoulder/maximum features in the $RrIi$ bands. Its spectral evolution is similar to that of HV SNe Ia, with a maximum-light Si II velocity of $15,000 pm 150 $km s$^{-1}$ and a post-peak velocity gradient of $sim$ $120 pm 10 $km s$^{-1} $d$^{-1}$. The Fe II and Mg II lines blended near 4300 {AA} and the Fe II, Si II, and Fe III lines blended near 4800 {AA} are obviously stronger than those of normal SNe Ia. Inspecting a large sample reveals that the strength of the two blends in the spectra, and the secondary peak in the $i/r$-band light curves, are found to be positively correlated with the maximum-light Si II velocity. Such correlations indicate that HV SNe~Ia may experience more complete burning in the ejecta and/or that their progenitors have higher metallicity. Examining the birthplace environment of SN 2017fgc suggests that it likely arose from a stellar environment with young and high-metallicity populations.
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