We present optical photometry and spectra for the Type Ia supernova (SN Ia) 2007gi in the nearby galaxy NGC 4036. SN 2007gi is characterized by extremely high-velocity (HV) features of the intermediate-mass elements (Si, Ca, and S), with expansion velocities (v_exp_) approaching 15500km/s near-maximum brightness (compared to 10600km/s for SNe Ia with normal v_exp_). SN 2007gi reached a B-band peak magnitude of 13.25+/-0.04mag with a decline rate of {DELTA}m15(B)(true)=1.33+/-0.09mag. The B-band light curve of SN 2007gi demonstrated an interesting two-stage evolution during the nebular phase, with a decay rate of 1.16+/-0.05mag/(100days) during t=60-90days and 1.61+/-0.04mag/(100days) thereafter. Such behavior was also observed in the HV SN Ia 2006X, and might be caused by the interaction between supernova ejecta and circumstellar material (CSM) around HV SNe Ia. Based on a sample of a dozen well-observed R band (or unfiltered) light curves of SNe Ia, we confirm that the HV events may have a faster rise time to maximum than those with normal v_exp_.