Noisy intermediate-scale quantum computers are widely used for quantum computing (QC) from quantum cloud providers. Among them, superconducting quantum computers, with their high scalability and mature processing technology based on traditional silicon-based chips, have become the preferred solution for most commercial companies and research institutions to develop QC. However, superconducting quantum computers suffer from fluctuation due to noisy environments. To maintain reliability for every execution, calibration of the quantum processor is significantly important. During the long procedure to calibrate physical quantum bits (qubits), quantum processors must be turned into offline mode. In this work, we propose a real-time calibration framework (RCF) to execute quantum program tasks and calibrate in-demand qubits simultaneously, without interrupting quantum processors. Across a widely used noisy intermediate-scale quantum (NISQ) evaluation benchmark suite such as QASMBench, RCF achieves up to 18% reliability improvement for applications. For reliability on different physical qubits, RCF achieves an average gain of 15.7% (up to 36.7%). For cloud quantum machines, the throughput can be improved up to 9.5 throughput per minute (6.5 on average) based on baseline calibration time. In conclusion, RCF offers a reliable solution for large-scale, long-serving quantum machines.