Accurate prediction of the spatial distribution of permeability of coal reservoirs using scare data from wells for coalbed methane exploration and development can lay a foundation for evaluating its gas production potential. By taking the #3 coal seam in the southern Shizhuang area in Qinshui Basin (Shanxi Province, China) as a research area, 23 key interpolation points that control the permeability of the coal seam were identified using a method that combines staged stripping of the structural stress field and structural curvature superposition. Permeability at the key interpolation points was calculated by combining the geological strength index (GSI) and regression of logging curve. The prediction method for spatial distribution of permeability (i.e., the combination of staged stripping of the structural stress field, determination of key interpolation points, and permeability prediction at key interpolation points) was developed. The differences in the spatial distribution of permeability using a key point and different methods (i.e., kriging interpolation method, intersection method of prospecting network at an equal interval, and random point selection for the same number of wells) were compared with that of 90 wells in the study area. The results indicate that the key control points for permeability of the coal seam can be identified by staged stripping of the structural stress field and structural curvature superposition: The permeability at the key interpolation points can be predicted by GSI. In addition, the key interpolation points can predict the high-value, sub-high-value, sub-low-value, and low-value zones of permeability of the coal seam in the study area using the same data points. The spatial distribution of permeability predicted by the key interpolation points was more accurate than that predicted by the intersection method of the prospecting network at an equal space and random point selection method, and it is closer to the predicted results using four sets of data. This research provides a method and reference for predicting changes in the permeability of a coal seam under limited drilling data.