We present extensive optical photometric and spectroscopic observations of the high-velocity (HV) Type Ia supernova (SN Ia) 2017fgc, covering the phase from similar to 12 days before to similar to 389 days after maximum brightness. SN 2017fgc is similar to normal SNe Ia, with an absolute peak magnitude of M-max(B) approximate to -19.32 +/- 0.13 mag and a post-peak decline of Delta m(15)(B) = 1.05 +/- 0.07 mag. Its peak bolometric luminosity is derived as (1.32 +/- 0.13) x 10(43) erg s(-1), corresponding to a Ni-56 mass of 0.51 +/- 0.03 M-circle dot. 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 +/- 150 km s(-1) and a post-peak velocity gradient of similar to 120 +/- 10 km s(-1) day(-1). The Fe II and Mg II lines blended near 4300 angstrom and the Fe II, Si II, and Fe III lines blended near 4800 angstrom 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.