By constructing a comprehensive evaluation index system of investment facilitation, this paper uses entropy method to measure the level of investment facilitation in 103 countries around the world, and uses the convergence model to analyze its spatial competition and convergence, and empirically tests the spatial effect of investment facilitation based on the spatial Durbin model. The article states that investment facilitation in countries around the world has steadily increased, but the dynamic evolution of the investment facilitation index in different types of countries is quite different. The level of investment facilitation in the countries not along Belt and Road and OECD countries is higher, but its characteristic differentiation is more obvious. There is spatial competition and convergence in the investment facilitation index and spatial factors can accelerate the convergence rate. The promotion of investment facilitation in the host country will not only significantly promote the growth of China’s outward foreign direct investment in the host country, but also has a significant spatial spillover effect, among which the spatial spillover effect of the business environment is the most obvious, followed by the spatial spillover effect of the financial service environment. The temporal and spatial characteristics of investment facilitation in host countries revealed in this paper provide an empirical basis for the high-quality development of China’s outward foreign direct investment.