  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.

High Energy Astrophysical Phenomena