The variation of the quench energy Ec (the minimum heat pulse energy required to destroy the superconductivity) of a composite superconductor with transport current is studied experimentally. The values of Ec for different types of composite are measured in a wide range of external magnetic fields B and transport currents I under different cooling conditions. It is shown that the values of Ec(I, B) satisfy a certain scaling law. This law allows one to put in order a large number of experimental data concerning the quench energy and to simplify the procedure of revealing the quench energy dependence on various parameters. A theoretical approach to interpretation of the scaling law is proposed. The results obtained may be of importance in the study of composite superconductor stability against thermal disturbances.