Attribute-Based Encryption (ABE) has emerged as an information-centric public-key cryptographic system which allows a data owner to share data, according to access policy, with multiple data users based on the attributes they possess, without knowing their identities. In the original ABE schemes, a central authority administrates the system and issues secret keys to data users based on their attributes and both the owner and users need to trust a specific CA. However, in certain real-world applications, the data users would not trust anyone but themselves. For such situations, we introduce a new decentralization model of ABE, termed Data User-based ABE (DU-ABE), which is managed jointly by the data users. DU-ABE is the first decentralized ABE scheme that replaces the authorities with the data users without employing any other extra entities.