SN 2019neq was a very fast evolving superluminous supernova. At a redshift z = 0.1059, its peak absolute magnitude was -21.5 ± 0.2 mag in g band. In this work, we present data and analysis from an extensive spectrophotometric follow-up campaign using multiple observational facilities. Thanks to a nebular spectrum of SN 2019neq, we investigated some of the properties of the host galaxy at the location of SN 2019neq and found that its metallicity and specific star formation rate are in a good agreement with those usually measured for SLSNe-I hosts. We then discuss the plausibility of the magnetar and the circumstellar interaction scenarios to explain the observed light curves, and interpret a nebular spectrum of SN 2019neq using published SUMO radiative-transfer models. The results of our analysis suggest that the spin-down radiation of a millisecond magnetar with a magnetic field $B\simeq 6\times 10^{14}\, \mathrm{G}$ could boost the luminosity of SN 2019neq.