A semi-butterfly connecting clamp and a building steel framework joint structure are mainly used for connection of a building steel framework. The connecting clamp includes a bearing plate, two L-shaped self-locking blocks, and two clamp wings provided at two ends of the bearing plate, respectively. Each of the clamp wings is integrally formed by a pre-tightening plate and a self-locking fastening plate. A groove is provided at an end of the self-locking fastening plate near the bearing plate. A wedge-shaped piece, having an inclined upper surface and a locking bolt hole, is placed on the self-locking fastening plate at a position near the groove. The retaining distance of the connecting clamp can be conveniently adjusted according to the size of the retained vertical column, and it can weaken the destruction action of the applied outside force on the building steel framework when the outside force acts on the connecting clamp.