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Photometric and spectroscopic observations of Type Ia supernova (SN) 2017fgc, which cover the period from -12 to + 137 d since the B-band maximum are presented. SN 2017fgc is a photometrically normal SN Ia with the luminosity decline rate, Delta m(15)(B)(true) = 1.10 +/- 0.10 mag. Spectroscopically, it belongs to the high-velocity (HV) SNe Ia group, with the Siii lambda 6355 velocity near the B-band maximum estimated to be 15200 +/- 480 km s(-1). At the epochs around the near-infrared secondary peak, the R and I bands show an excess of similar to 0.2-mag level compared to the light curves of the normal velocity (NV) SNe Ia. Further inspection of the samples of HV and NV SNe Ia indicates that the excess is a generic feature among HV SNe Ia, different from NV SNe Ia. There is also a hint that the excess is seen in the V band, both in SN 2017fgc and other HV SNe Ia, which behaves like a less prominent shoulder in the light curve. The excess is not obvious in the B band (and unknown in the U band), and the colour is consistent with the fiducial SN colour. This might indicate that the excess is attributed to the bolometric luminosity, not in the colour. This excess is less likely caused by external effects, like an echo or change in reddening but could be due to an ionization effect, which reflects an intrinsic, either distinct or continuous, difference in the ejecta properties between HV and NV SNe Ia., Turkish Scientific and Technical Research Council [TUBITAK-2211C, 2214A]; TUBITAK [17BT60-1185, 120F169]; JSPS KAKENHI [JP20H00174, JP20H0473, JP18H04585, JP18H05223, JP17H02864], We acknowledge ESA Gaia, DPAC, and the Photometric Science Alerts Team (http://gsaweb.ast.cam.ac.uk/alerts).Umut Burgaz acknowledges the support provided by the Turkish Scientific and Technical Research Council (TUBITAK-2211C and 2214A). The authors thank TUBITAK for a partial support in using T60 telescope with the project number 17BT60-1185. Keiichi Maeda acknowledges support by JSPS KAKENHI Grant (JP20H00174, JP20H0473, JP18H04585, JP18H05223, and JP17H02864). Belinda Kalomeni acknowledges support by TUBITAK (Project no: 120F169). The authors thank the anonymous referee for her/his valuable comments and suggestions that have significantly improved the manuscript.