The invention relates to a superconductive current limiting based no-arc DC breaker and a breaking method thereof. The breaker comprises a disconnecting switch unit, a superconductive current limiting unit and a no-arc breaking unit in serial connection; the superconductive current limiting unit includes a resistive type superconductive current limiter, and the no-arc breaking unit comprises a mechanical switch, a current converting capacitor and an energy absorbing branch; when a fault occurs, the superconductive current limiting unit quenches superconductivity to limit a short-circuit current, and a rising voltage at the two ends serves as a control signal for motion of the mechanical switch of the no-arc breaking unit; after that the no-arc breaking unit receives the control signal, the DC is disconnected; and finally, the disconnecting switch unit is disconnected in zero current. According to the invention, the superconductive current limiting unit limits the short-circuit current, the charging speed of a current converting capacitor is reduced, and due to that the voltage of the mechanical switch equals that of the current converting capacitor, the voltage of the mechanical switch is lower than a voltage to maintain an arc in certain stage of the disconnecting process, and the arc cannot be generated and is quenched rapidly; and at the same time, the superconductive current limiting unit inhibits voltage and current oscillation in the capacitor, and prevents generation of overvoltage.