Cloud computing is one of the most important and promising technologies. Data owners can outsource their sensitive data in a cloud and retrieve them whenever and wherever they want. But for protecting data privacy, sensitive data have to be encrypted before storing, which abandons traditional data utilization based on plaintext keyword search. Around the multi-keyword fuzzy matching and data security protection problems, we propose a multi-keyword fuzzy search method on the encrypted data. Based on the Bloom filter, our scheme uses dual coding function and the position sensitive Hash function to build file index. In the meantime, it uses the distance recoverable encryption arithmetic to encrypt the file index, consequently achieving the function which is facing the multi-keyword to fuzzy search over the encrypted data. Meanwhile, the scheme does not need to set index storage space in advance, which greatly reduces the complexity of the search. Compared with the existing solutions, the scheme does not need predefined dictionary library which lowers the storage overhead in consequence. Experimental analysis and security analysis show that the proposed scheme not only achieves the multi-keyword fuzzy search over the encrypted data, and guarantees the confidentiality and privacy.