As for attribute-based access control in cloud storage, most of researches focus on reading permission control when multiple users read the same out-sourced data simultaneously. They dot’t consider writing permission control when multiple users modify the same data simultaneously. In multi-user collaborative edit scene, challenges have emerged: 1) A data owner with limited capabilities of computation, storage and communication, would like cloud to aid him with writing permission control, but would not like it to know the content of data, or get what is matched, or even predict the users’ writing permission either. 2) Boolean formula cannot describe writing permission policy. 3) Bilinear pairing operations bring great computational costs. In this work, a collaborative edit access control method is presented in cloud storage. That is, a data owner defines writing permission policy represented by a circuit, and semi-trusted cloud decides whether or not the writing succeeds by matching writing policy without the prediction of acceptability of the next edit request. Analyses and simulations show that our method is provided with the ability of multi-user collaborative access control for cloud storage, and the storage cost and the computation cost of encrypting and decrypting are both lesser at user end in reading permission control with cloud-aided decryption.