The construction of ecological spatial networks is a common method used to optimize the regional landscape structure and enhance ecosystem service functions. However, the relationship between the structure of ecological spatial networks and specific ecosystem service functions is still rarely explored. Based on multi-source remote sensing data products and with the western region of Handan as the study area, the spatiotemporal evolution characteristics of carbon sequestration function and ecological spatial networks were analyzed, and the correlation between the topological structure characteristics of ecological spatial networks and carbon sequestration function was studied. The results showed that from 2000 to 2020, the average NPP value in the study area was 2.17×108 kg/(m2·a), which showed a significant upward trend. The overall connectivity of the ecological spatial network in the study area was high, with a clear community structure and an extreme level of unevenness. The connectivity of the network was basically stable during the research period, but the heterogeneity was slighted increased. There was a significant positive correlation between the network’s topological indicators and their carbon sequestration function in the study area. Among them, the correlation of node betweenness was the most significant, followed by PageRank and degree. These three indicators may be potential effective indicators for judging the carbon sequestration function of nodes in ecological spatial networks. The research results had important reference value for the construction and optimization of ecological spatial networks and the improvement of regional carbon sequestration function.