In order to solve the safety problems of privacy in the processes of authentication and communication of Radio Frequency IDentification (RFID) system, a mutual authenticate and encrypt scheme with low resource consume, high-level security and applicable for most of RFID systems was designed. This scheme combined the improved Elliptic Curve Diffie-Hellman (ECDH) algorithm and Advanced Encryption Standard (AES) algorithm to implement functions of key distribution, certification and communication encryption. It used dynamic key to enhance security. In addition, this scheme reduced the operation scale with original security strength, and saved the overhead of system resources. The measured results show that this scheme can resist replaying attacks, impersonation attacks, man-in-the-middle attacks and Denial of Service (DoS) attacks so as to save system resources. It can be applied in the field of Internet of Things (IOT) which has requirements on security and costs.