This paper reports simulation of L–H transition by fluid transport code B2SOLPS0.5.2D at low ion plasma density on neutral beam injection (NBI) in the edge plasma of small size divertor tokamak. The simulation provides the following results: (1) the transition is possible at plasma density 2 × 1019 m−3 with NBI at temperature heating Theating 3.62 keV. (2) The simulation predicts the generation of large negative radial electric field Er, which is thought to help L–H transition during NBI, is suggested in the edge plasma of small size divertor tokamak. (3) The toroidal current density in the edge plasma of small size divertor tokamak is plasma density and direction of NBI dependence. (4) Parallel flux transport by anomalous viscosity (turbulent) through separatrix leads to the variation of toroidal current density.