The invention provides a multi-laser-head laser cutting machine. The multi-laser-head laser cutting machine comprises a workbench, a laser cutting control system, a CO2 laser generator, a CO2 laser power supply, a CO2 laser reflector, at least one non-CO2 laser generator, for example, a fiber laser generator, a multi-laser-head cutting assembly, an X-axis movement assembly, a Y-axis movement assembly, a Z-axis movement assembly, a laser generator cooling system, an object carrying working table, a cutter console, a waste material collecting device and a dust collecting exhaust fan. Two or more than two laser sources are combined on the same laser cutting equipment by the multi-laser-head cutting assembly, so that the cutting processing of composites and the cutting processing of different single materials are realized.