Data access control in a cloud storage system is regarded as a promising technique for enhanced efficiency and security utilizing a ciphertext-policy attribute-based encryption (CP-ABE) approach. However, due to a large number of data users as well as limited resources and heterogeneity of data devices in Internet of Things (IoT), existing access control schemes for the cloud storage are not effectively applicable to IoT applications. In this article, we construct a new CP-ABE-based storage model for data storing and secure access in a cloud for IoT applications. Our new framework introduces an attribute authority management (AAM) module in the cloud storage system functioned as an agent that provides a user-friendly access control and highly reduces the storage overhead of public keys. Then, we propose a novel secure and efficient multiauthority access control scheme of the cloud storage system for IoT, namely, SEM-ACSIT, which obtains both backward security and forward security when an attribute of a user is revoked. By exploiting encryption outsourcing, simplified key structuring and the AAM module, the computational overhead of a user is immensely decreased. Moreover, a user access control list (UACL) in the cloud server is constructed newly to support authorization access for a specific user. The analysis and simulation results demonstrate that our SEM-ACSIT scheme achieves powerful security with less computational overhead and lower storage costs than the existing schemes.