With the rapid development of cloud storage, more and more people prefer to transfer personal files and data from local to cloud and share them with each other by cloud storage service. Nevertheless, each user has different access privileges on account of different identities, roles, etc. Given the different access privileges among the multi-user sharing the same file in cloud environment, an efficient file sharing scheme for multi-user is presented. Based on Elgamal cryptographic system and proxy re-encryption, multi-user access to different contents of the same file encrypted once by file owner is achieved in the proposed scheme. Compared with previous proposals, the scheme has the following advantages: the computation of the shared file encrypted by file owner is only proportional to the exponentiations of the amount of file blocks, regardless of bilinear pairings. Besides, users access to different contents of the same file by exponentiations with linear times regardless of bilinear pairings. Furthermore, ciphertext space for storage has no increments. Further analysis shows that our scheme adapts to the characteristics of cloud computing, which means cloud service providers provide fast computation and huge storage for thin clients.