Because of the rapid growth of cloud computing and the expansion of mobile phone users in recent years, mobile cloud computing has attracted wide attention. In the mobile cloud, wireless computing networks are the basics of sharing data between mobile devices and cloud services. Since air is the communication medium, it must be properly protected; otherwise, it will be subject to a variety of security threats, for example, attacks from middle-man, identity tracking, etc... Furthermore, mobile devices are limited in storage, resources, and computing powers. Hence, designing an efficient and secure balance of authentication schemes is extremely important. First of all, a multi-factor authentication scheme based on biometric (fingerprint information), hash function, and fuzzy vault algorithm is presented in that paper. Secondly, the Validation and Analysis tool of AVISPA Security was approved. Thirdly, the security of the scheme proposed is compared to other related schemes.