Cloud radio access network (C-RAN) has emerged as a potential candidate of the next generation access network technology to address the increasing mobile traffic, while mobile cloud computing (MCC) offers a prospective solution to the resource-limited mobile user in executing computation intensive tasks. Taking full advantages of above two cloud-based techniques, C-RAN with MCC are presented in this paper to enhance both performance and energy efficiencies. In particular, this paper studies the joint energy minimization and resource allocation in C-RAN with MCC under the time constraints of the given tasks. We first review the energy and time model of the computation and communication. Then, we formulate the joint energy minimization into a non-convex optimization with the constraints of task executing time, transmitting power, computation capacity and fronthaul data rates. This non-convex optimization is then reformulated into an equivalent convex problem based on weighted minimum mean square error (WMMSE). The iterative algorithm is finally given to deal with the joint resource allocation in C-RAN with mobile cloud. Simulation results confirm that the proposed energy minimization and resource allocation solution can improve the system performance and save energy.