QFaaS is a Quantum Function-as-a-Service framework that leverages the advantages of the serverless computing model and state-of-the-art software engineering techniques to advance practical quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era. Our framework provides essential elements of a serverless quantum system to streamline service-oriented quantum application development in cloud environments, such as combining hybrid quantum-classical computation, automating the backend selection, and adapting Quantum DevOps workflow. QFaaS offers the first full-stack and unified quantum serverless platform by integrating multiple well-known quantum software development kits, quantum simulators, and quantum cloud providers (IBM Quantum and Amazon Braket).