We propose a scenario which can explain large lepton asymmetry and small baryon asymmetry simultaneously. Large lepton asymmetry is generated through the Affleck-Dine (AD) mechanism and almost all the produced lepton numbers are absorbed into Q-balls (L-balls). If the lifetime of the L-balls is longer than the onset of electroweak phase transition but shorter than the epoch of big bang nucleosynthesis (BBN), the large lepton asymmetry in the L-balls is protected from sphaleron effects. On the other hand, small (negative) lepton numbers are evaporated from the L-balls due to thermal effects, which are converted into the observed small baryon asymmetry by virtue of sphaleron effects. Large and positive lepton asymmetry of electron type is often requested from BBN. In our scenario by choosing an appropriate flat direction in the minimal supersymmetric standard model, we can produce positive lepton asymmetry of the electron type but totally negative lepton asymmetry.