The superconducting inductive pulsed-power supply (SPPS) circuit consists of a high-temperature superconducting pulsed-power transformer (HTSPPT) and an auxiliary capacitor. The electrical losses and the power of the primary source can be cut down with the superconducting inductive energy storage. Although its energy density is slightly less than a purely superconducting inductive system, it can reduce the maximum voltage of the opening switch by the capacitor and achieve a high degree of current amplification factor. However, during the discharge process, the magnetic leakage flux energy stored in the primary of the HTSPPT requires the capacitor to have a certain capacity. The higher the ratio of the capacitive stored energy over the total inductive stored energy, the more the dominant position of inductive energy storage reduces. The current amplification factor ( $\gamma $ ), the maximum voltage of the opening switch ( $V_{S\max }$ ), and the ratio of capacitive stored energy ( $\eta $ ) are the three main properties of the SPPS circuit, which depends on several intertwined critical parameters, such as the inductance ratio $n = L_{2}$ /( $L_{2}+L_{L}$ ) and the capacitance ( $C_{{\mathbf {1}}}$ ). This paper studies the influence of the critical parameters on the main circuit performance with a 1-kJ SPPS system. The detailed selection method of the critical parameters for the specific system is also discussed with a coupling coefficient of 0.95. Such a system is easy to be utilized for the basic experimental study of a small railgun.