The stability of a new adiabatic circuit with inductive load is discussed. The adiabatic circuit generates quasi-sinusoidal waveform current with multiple power-supply voltages. SPICE simulation shows that this circuit is stable after damping oscillation. For the analytical discussion, we derive a matrix that connects charge, current, and voltage in the circuit. By using matrix theory and a physical consideration, it is proved that the absolute value of the eigen value of the matrix, which connects the initial voltage and current deviations from the equally-divided-stepwise mode with those after the charge-recycling process, is smaller than 1. Therefore, the voltage and current deviations become zero after many charge-recycling processes. The circuit might be useful for a DC-AC inverter in the power electronics.