As an expansion area of international cooperation under the Belt and Road Initiative, South America is of great importance for China to enhance geo-economic status and expand geo-economic space. Based on trade, investment, tourism, transportation and politics, this paper establishes a multi-dimensional index system of geo-economic linkages intensity and analyzes the important characteristics of the geo-economic linkages intensity between China and countries in South America by using the gray correlation TOPSIS method and geographically weighted regression model. The results show that: (1) The geo-economic flows between China and South American countries show an overall increasing trend during 2006-2015. (2) China and South American countries have an unbalanced development in geo-economic linkages elements. The geo-economic linkage of transportation is higher than that of politics, tourism, investment and trade. (3) The geo-economic linkages intensity between China and South American countries are at a low level and varies significantly among countries. (4) The geo-economic linkages intensity between China and South American countries is slowly increasing, and the changes in spatial pattern are small year by year. (5) Gross domestic product, population size and cooperative goldenstein factor are the dominant factors influencing the geo-economic linkages intensity between China and countries in South America. Market is the most important driving force for geo-economic linkages intensity between China and countries in South America. Resource endowment has little effect on the geo-economic linkages intensity, while geopolitics has a significant effect on the geo-economic linkages intensity.