We explore a novel possibility that dark matter has a light mass below 1 GeV in a lepton portal dark matter model. There are Yukawa couplings involving dark matter, left-handed leptons and an extra scalar doublet in the model. In the light mass region, dark matter is thermally produced via its annihilation into neutrinos. In order to obtain the correct relic abundance and avoid collider bounds, a neutral scalar is required to be light while charged scalars need to be heavier than the electroweak scale. Such a mass spectrum is realized by adjusting quartic couplings in the scalar potential or introducing an extra singlet scalar. We also discuss the signals of our model at the LHC.