Current flow through an InGaN/GaN/AlGaN multi-quantum well (MQW) laser diode is simulated. We found that electron overflow to the AlGaN p-cladding layer is very large, which prevents the current injection into the MQW layers. We clarified that the electron overflow occurs easily in nitride lasers because of three intrinsic reasons; poor hole injection due to the small hole mobility and thermal velocity, the small conduction band offset for InGaN/GaN, and the high threshold carrier density. We show that the Al composition and the p-doping of the AlGaN p-cladding layer is of critical importance to obtain laser oscillation by current injection.