In a frozen inert gas plasma (FIP) MHD power generation, the influence of load resistance on the performance, the comparison of the performance with r-θ two-dimensional numerical simulation, and the effect of the non-uniformity of inlet plasma along the direction perpendicular to walls on the performance are examined with r-z two-dimensional numerical simulation. For a low load resistance, the efficiency is reduced because the ionization degree of inert gas ions cannot be kept constant up to the downstream channel. On the other hand, for a high load resistance, the efficiency is reduced owing to the development of the boundary layer. As a result, the optimal load resistance exists. In comparison with r-θ two-dimensional numerical simulation without the boundary layer, the performance estimated from the present r-z two-dimensional numerical simulation can deteriorate, and the optimal inlet ionization degree decreases, while the optimal load resistance increases. The enthalpy extraction ratio increases when the inlet ionization degree in the main flow is higher than that near the walls, while it decreases for the inverse distribution at the inlet, even if the introduced total inlet ionization degree is the same. Here results are attributed to the development of boundary layer.