Aiming at failure mechanisms and judgment criterion of progressive collapse for space trusses, the responses and the failure mechanisms of diagonal square pyramid space trusses, leaning laid pyramid space trusses and orthogonal square pyramid space trusses with circumferential simple supports under different seismic waves were analyzed in this paper. The results show that space trusses have a good performance of earthquake resistance, but progressive collapse occurs easily. Based on the failure mechanisms of space truss, a judgment criterion of space truss is proposed under strong earthquakes, according to the characteristics of energy, displacements and plastic levels of members. The judgment criterion is expressed by judgment coefficient J. When J>6, space trusses tend to be ductile failure, however, When J> 6, space trusses tend to be progressive collapse.