We present extensive optical photometric and spectroscopic observations of the high-velocity (HV) Type Ia supernova (SN Ia) 2017fgc, covering the phase from ~12 days before to ~389 days after maximum brightness. SN 2017fgc is similar to normal SNe Ia, with an absolute peak magnitude of M_max_^B^~-19.32+/-0.13mag and a post-peak decline of {Delta}m_15_(B)=1.05+/-0.07mag. Its peak bolometric luminosity is derived as (1.32+/-0.13)x10^43^erg/s, corresponding to a 56Ni mass of 0.51+/-0.03M_{sun}_. 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 SiII velocity of 15000+/-150km/s and a post-peak velocity gradient of ~120+/-10km/s/day. The FeII and MgII lines blended near 4300{AA} and the FeII, SiII, and FeIII 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 SiII 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.