Research on policy diffusion mechanism of Government Procurement of Public Services (GPPS) is beneficial to improve the efficiency of policy formulation and implementation. In view of four dimensions which are internal demand, external pressure, policy innovation environment and service characteristic, a system of factors affecting policy diffusion is established. On this basis, a Multilayer Fuzzy Cognitive Map (MFCM) model for policy diffusion of GPPS is constructed. Nonlinear Hebbian Learning algorithm and genetic algorithm are applied to optimize the two components of MFCM model, which are relationship between nodes at the same layer and influence weights between nodes at different layers respectively. Taking Nanjing municipal government purchasing elderly-care services in China as the empirical object, simulation of policy diffusion based on MFCM model is carried out, aiming to obtain the key factors influencing policy diffusion and the dynamic diffusion mechanism of GPPS policy. Research results show that, compared with monolayer Fuzzy Cognitive Map, MFCM model converges faster. In addition, simulation results of policy diffusion indicate that economic development level of jurisdiction, superior pressure, administrative level and operability of services are key influencing factors which are under four dimensions correspondingly. And the dynamic influencing mechanism of key factors has also been learned.