Helium is expected to be present in the massive ejecta of some hydrogen-poor superluminous supernovae (SLSN-I). However, until now only one event has been identified with He features in its photospheric spectra (PTF10hgi). We present the discovery of a new He-rich SLSN-I, ZTF19aawfbtg (SN2019hge), at z = 0.0866. This event has more than 10 optical spectra at phases from −41 to +103 days relative to the peak, most of which match well with that of PTF10hgi. Confirmation comes from a near-IR spectrum taken at +34 days, revealing He i features with P-Cygni profiles at 1.083 and 2.058 m. Using the optical spectra of PTF10hgi and SN2019hge as templates, we examined 70 other SLSNe-I discovered by Zwicky Transient Facility in the first two years of operation and found five additional SLSNe-I with distinct He-features. The excitation of He i atoms in normal core-collapse supernovae requires nonthermal radiation, as proposed by previous studies. These He-rich events cannot be explained by the traditional 56Ni mixing model because of their blue spectra, high peak luminosities, and long rise timescales. Magnetar models offer a possible solution since pulsar winds naturally generate high-energy particles, potential sources of nonthermal excitation. An alternative model is the interaction between the ejecta and dense H-poor circumstellar material, which may be supported by observed undulations in the light curves. These six SLSNe-Ib have relatively low-peak luminosities (rest frame Mg = −20.06 0.16).