Broadcast encryption provides a promising technique of data access control for specified users in cloud computing. A data uploader can generate a ciphertext for a set of chosen users such that only the intended users are able to access the data. However, with the rapidly increasing of collaboration between users, it is desired to extend the receiver set to grant decryption right for more users. The existing broadcast encryption systems cannot support receiver extension. In this article, we for the first time take this problem into consideration and give a solution. We take the merits of identity-based cryptosystem and propose a notion of EIBBE: a flexible data access control with receiver extendable for cloud computing based on broadcast encryption. It allows the authorized user to extend the receiver set <inline-formula><tex-math notation="LaTeX">$S$</tex-math></inline-formula> stated in the IBBE ciphertext by adding a new receiver set <inline-formula><tex-math notation="LaTeX">$S^{\prime }$</tex-math></inline-formula> without re-encryption. Both the users in <inline-formula><tex-math notation="LaTeX">$S$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$S^{\prime }$</tex-math></inline-formula> can access the data successfully. Moreover, the data uploader determines the maximum number of extended receivers. We then give a concrete construction of EIBBE and provide a rigorous security analysis of our proposed scheme. Finally, we demonstrate the scheme's efficiency and feasibility.