Mobile cloud computing uses features to deliver outsourcing data to remotely available mobile devices. However, the flexible nature of the mobile device is a critical challenge for the mobile cloud computing environment. The mobile phone significantly degrades the data transfer performance when initiating the handover process. Thus, an energy-efficient handover process could improve the quality of service (QoS). Here, we introduce a secure energy-efficient and quality-of-service architecture (EEQoSA) for the handover process in the mobile cloud computing environment. The proposed architecture involves four layers: application, the Internet protocol multimedia subsystem (IPMS), communication, and media with connectivity layers. These four layers collectively handle the energy-efficiency, security and QoS parameters. Existing service-oriented architectures designed for mobile cloud computing are based on the symmetric encryption cryptography to support different media services. However, this approach easily allows an adversary to expose the symmetric key and gain access to private data. Thus, our proposed architecture uses the secure and strong authentication (SSA) process at the IPMS layer by protecting the media services from unauthorized users, as the IPMS is the central layer that could be the entry point for an adversary. Furthermore, to extend the mobile lifetime during the handover process, an energy detection (ED) model is deployed at the communication layer to detect the energy level of the mobile device prior to the handover initialization process. The media with the connectivity layer supports the secure handover process using a priority enforcement module that allows only legitimate users to complete the re-registration process after initiating the handover. Finally, the architecture is tested using the CloudSim simulation environment and validated by a comparison with other known service-oriented architectures.