The collaboration of scientists is important for promoting the scientific development and technological progress of a country, and even of the world. Based on the cooperation data of academicians of the Chinese Academy of Sciences (CAS) in the China National Knowledge Infrastructure (CNKI), we portray the scientific cooperation network of Chinese scientists using Pajek, Gephi, ArcGIS, and other software, and the complexity of the scientific cooperation network of Chinese scientists and its proximity mechanism are explored by combining complex network analysis, spatial statistical analysis, and negative binomial regression models. Our main conclusions are as follows: (1) In terms of network structure, the scientific cooperation network of Chinese scientists has a multi-triangular skeleton, with Beijing as its apex. The network has an obvious hierarchical structure. Beijing and Shanghai are located in the core area, and 16 cities are located in the semi-periphery of the network, while other cities are located at the periphery of the network. (2) In terms of spatial distribution, the regional imbalance of the scientific cooperation of Chinese scientists is obvious. Beijing–Tianjin–Hebei, the Yangtze River Delta, and the central-south region of Liaoning are hot spots for the scientific research activities of Chinese scientists. (3) The negative binomial regression model accurately explains the proximity mechanism of the scientific cooperation network of Chinese scientists. The geographical proximity positively affects the scientific cooperation of Chinese scientists under certain conditions. The educational proximity is the primary consideration for scientists to cooperate in scientific research. The closer the educational level of the cities, the greater the cooperation. Economic and social proximity can promote scientific cooperation among scientists, whereas institutional proximity negatively and significantly affects scientific cooperation.