In the base station cooperation system, the centralized cooperative pre-coding based on regularized zero-forcing beam-forming (RZFBF) could obtain a similar capacity performance to that of dirty-paper coding. However, with the number of cooperative base station increasing, the centralized cooperative pre-coding had a quite high requirement for the backhaul capacity. In order to solve this problem, a distributed transmitted signal design scheme based on generalized approximate message passing (GAMP) algorithm was proposed. The scheme decomposed the overall compucentralized RZFBF pre-coding problem into a problem of signal estimation by constructing a virtual linear communication system, and decomposes the overall computational cost into many smaller computation tasks by exchanging information between adjacent base stations, which greatly reduced the requirement of backhaul capacity. Simulation results showed that the proposed algorithm could achieve approximate system tjroughput with the centralized cooperative RZFBF pre-coding at a lower computational complexity.