For a self-field magnetoplasmadynamic (MPD) thruster using hydrogen propellant, plasma flows were numerically simulated with a model including the ion-slip effect. To clarify the thruster behavior near the critical current, the discharge current and the propellant mass flow rate were set to 5 or 10 kA (critical current) and 0.4 g/s, respectively. At the critical current, current paths protruded toward a downstream region due to an increased Hall parameter when compared with the lower current case. In conjunction with this, the pressure was higher in the vicinity of the cathode tip and the ion-slip parameter exceeded unity in the discharge chamber at the critical current. Significant ion-slip heating occurred in the supersonic region, which resulted in limited amount of gas dynamic thrust.