The growing requirement of data-intensive computing makes the problem of insufficient memory bandwidth more critical. The advantages of multicore architectures and advanced parallel computers are limited. The new kind of architecture, Processor-in-Memory (PIM), is developed to solve the above challenge by integrating the computing logics and tiny processors into the DRAM chip. The data processing capability of the memory subsystem can be improved. However, the bandwidth of the conventional interconnection networks can not satisfy the bandwidth consumption of multiple PIM modules. Therefore, a new memory network, MemGrid, is proposed for connecting multiple PIM memory modules and CPUs. The proposed MemGrid network has the capabilities of high scalability and low diameter. The connection topologies of MemGrid network with the corresponding network switch architecture are discussed. The experimental results show that the MemGrid network can achieve better performance than other interconnection networks in variant accessing patterns and configurations.