Authentication and authorization constitute the essential security component, access control, for preventing unauthorized access to cloud services in mobile cloud computing (MCC) environments. Traditional centralized access control models relying on third party trust face a critical challenge due to a high trust cost and single point of failure. Blockchain can achieve the distributed trust for access control designs in a mutual untrustworthy scenario, but it also leads to expensive storage overhead. Considering the above issues, this work constructed an authentication and authorization scheme based on blockchain that can provide a dynamic update of access permissions by utilizing the smart contract. Compared with the conventional authentication scheme, the proposed scheme integrates an extra authorization function without additional computation and communication costs in the authentication phase. To improve the storage efficiency and system scalability, only one transaction is required to be stored in blockchain to record a user’s access privileges on different service providers (SPs). In addition, mobile users in the proposed scheme are able to register with an arbitrary SP once and then utilize the same credential to access different SPs with different access levels. The security analysis indicates that the proposed scheme is secure under the random oracle model. The performance analysis clearly shows that the proposed scheme possesses superior computation and communication efficiencies and requires a low blockchain storage capacity for accomplishing user registration and updates.