We have been studying a superconducting quantum-computing system where superconducting qubits are controlled and read out by rapid single-flux- quantum (RSFQ) circuits. In this study, we designed and fabricated an RSFQ microwave chopper, which turns on and off an externally applied microwave to control qubit states with the time resolution of sub-nanosecond. The chopper is implemented in a microwave module and mounted in a dilution refrigerator. We tested the microwave chopper at 4.2K. The amplitude of the output microwave was approximately 100μV which is much larger than that of previously designed chopper. We also confirmed that the irradiation time can be controlled by RSFQ control circuits.