Cloud storage is an extension concept of cloud computing and has become an interested research topic since it is convenient and cheap in many applications. In this paper, we propose a new fully distributed cloud storage model together with the attribute-based encryption technology. There are three phases in our model: the encryption phase, the data storage phase and the decryption phase. All messages in these phases are distributed through the whole process. In the encryption stage, the data owner encrypts data blocks based on attribute based encryption, and then sends each encrypted block to several random storage servers. We use the distributed erasure code to guarantee the robustness of our model in the storage phase. Our model supports one-to-many storage. Furthermore, it does not require any trusted authority since we adopt a multi-thority model in which all authorities work in each phase indpendently. We also analyze the reliability and security of our model.