To improve low-latency computing and communication services, a new type of mobile edge computing architecture named multi-layer cloud radio access network (Multi-layer CRAN) is designed in this paper. In Multi-layer CRAN, a high-level edge cloud is deployed next to base band unit pool to handle the computing tasks of user equipment (UE) in centralized way. Meanwhile, a low-level edge cloud is deployed in each remote radio head (RRH) to locally handle UEs’ computing tasks in a distributed way. Based upon Multi-layer CRAN, a cooperative communication and computation resource allocation (3C-RA) algorithm is further designed for lower service latency and energy cost, and higher network throughput in this paper. 3C-RA utilizes a distributed RRH cell coloring algorithm to enable each RRH to work out the resource allocation in an efficient and distributed way. 3C-RA employs a proportional fairness-based approach to allocate communication and computation resource in each RRH cell. A series of simulations on Multi-layer CRAN with 3C-RA were carried out. The simulation results validate that Multi-layer CRAN is more capable of providing low-latency computing and communication services, and 3C-RA enables Multi-layer CRAN to have lower service latency and energy cost and higher network throughput.