At the present, participants in the multimedia mobile edge computing (MMEC) environment encrypt multimedia data when the Terminal communicates with mobile edge computing cloud or central cloud, ensuring data confidentiality and transmission security. However, there is no authentication of the platform identities' authenticity for participants and verification of the devices' integrity; this is a challenging problem. Therefore, this paper proposes a novel remote attestation model and protocol for the security of MMEC, namely MMECRA model and protocol. Firstly, participants from the MMECRA model and protocol execute some operations to comprehensively guarantee data security, platform identity security, and integrity state-maintained, such as mutual identity anonymous authentication, mutual integrity measurement, and mutual integrity verification operations. Then, the formal analysis with Burrows-Abadi-Needham (BAN) logic and the analysis of important security performance show that the protocol is superior to the existing security schemes in terms of privacy protection ability and anti-attack ability. Moreover, the simulation results demonstrate that the MMECRA protocol in the state of non-intensive multimedia resource requests can effectively reduce the computational cost.