To study the progressive collapse of a prefabricated reinforced concrete frame structure (PRCS) with steel tube bolted connection, three full-scale prefabricated long columns were tested. First, a simplified prefabricated column model was proposed by using the multi-stage linear plastic connection element in SAP2000. The column-column joint was simulated and compared with test results. Then, a six-story PRCS connected by steel tube bolted bars and a six-story cast-in-place reinforced concrete frame structure (CRCS) were analyzed by removing column method. Four working conditions were removed, namely, the corner column, the long side middle column, the short side middle column, and the inner column of the first floor. The internal force and displacement time history curve of key components were obtained after removing the columns. Lastly, the collapse mechanisms of PRCS and CRCS were analyzed through Pushdown curves. Results show that the multi-stage linear plastic connection element well simulated the prefabricated column-column joint, and the simulation value was consistent with the test value. Under design load, the failure of the inner column had the greatest impact on the PRCS, and its displacement was 72.2% larger than that of the CRCS. By analyzing the Pushdown curves, it was found that when the corner column was damaged, the bearing capacity of the PRCS under beam mechanism was the lowest, which was 25.4% less than that of CRCS, and the lowest bearing capacity was 33.1% less than that of CRCS when the inner column was damaged. Finally, the section size and reinforcement of the inner and side columns and their adjacent beam members that are needed to be strengthened, as well as the thickness of the outer steel tube, were obtained to improve their rigidity. Therefore, this paper can provide reference for the collapse resistance design of the subsequent engineering application of such prefabricated structures.