  We present a self-interacting boosted dark matter (DM) scenario as a possible
explanation of the recently reported excess of electron recoil events by the
XENON1T experiment. The Standard Model (SM) has been extended with two
vector-like fermion singlets charged under a dark $U(1)_D$ gauge symmetry to
describe the dark sector. While the presence of light vector boson mediator
leads to sufficient DM self-interactions to address the small scale issues of
cold dark matter, the model with sub-GeV scale DM can explain the XENON1T
excess via elastic scattering of boosted DM component with electrons at the
detector. Strong annihilation of DM into the light mediator leads to a
suppressed thermal relic. A hybrid setup of dark freeze-out and non-thermal
contribution from the late decay of a scalar can lead to correct relic
abundance. We fit our model with XENON1T data and also find the final parameter
space consistent with self-interaction of DM, DM-electron scattering rate, as
well as astrophysical and cosmological observations. A tiny parameter space
consistent with all these constraints and requirements can be further
scrutinized in near-future experiments.
