Based on the gravity model and the cohesive subgroup analysis of social network analysis, this paper makes an exploration on the spatial relations of innovation output in 31 provinces. It is found that the spatial linkage of innovation output in China mainly centers on the areas of Beijing Tianjin Hebei and Yangtze River Delta, showing a serious uneven distribution, with strong regional concentration and spatial dependence. Beijing, Tianjin, Shanghai, Zhejiang and Jiangsu, as nodes of regional innovation and output, have stronger radiation effects on the surrounding regions. Overall, the spatial linkage does not form a cross network structure that runs through the four corners of our country. In addition, the number of central provinces, districts and cities is small and the distribution is uneven, and the range of radiation is limited. Therefore, the paper puts forward some policy proposals to increase regional innovation input, reduce policy barriers to regional innovation output, and create a good environment for regional innovation output linkage.