We present the early-phase spectra and the light curves of the broad-lined (BL) supernova (SN) 2016coi from t = 7 to 67 days after the estimated explosion date. This SN was initially reported as a BL Type SN Ic (SN Ic-BL). However, we found that spectra up to t = 12 days exhibited the He i λ5876, λ6678, and λ7065 absorption lines. We show that the smoothed and blueshifted spectra of normal SNe Ib are remarkably similar to the observed spectrum of SN 2016coi. The line velocities of SN 2016coi were similar to those of SNe Ic-BL and significantly faster than those of SNe Ib. Analyses of the line velocity and light curve suggest that the kinetic energy and the total ejecta mass of SN 2016coi are similar to those of SNe Ic-BL. Together with BL SNe 2009bb and 2012ap, for which the detection of He i was also reported, these SNe could be transitional objects between SNe Ic-BL and SNe Ib, and be classified as BL Type "Ib" SNe (SNe "Ib"-BL). Our work demonstrates the diversity of the outermost layer in BL SNe, which should be related to the variety of the evolutionary paths.