Random oracle model is a general security analysis tool for rigorous security proof and effective cryptographic protocol design. In the quantum world, the attempts of constructing a quantum random oracle (QRO) have been made, such as quantum-accessible random oracle for post-quantum cryptography and quantum random oracle for quantum cryptography. To facilitate the security analysis of quantum cryptographic protocols, we introduce quantum random oracle. As in the classical circumstance, it is crucial and challenging to design and instantiate the QRO model with an appropriate quantum hash function. As a result, we use the QRO model for the security analysis of quantum public-key encryption and quantum digital signature.