Very large current composite superconductors have been considered and adopted to use in SMES coils and fusion applications, such as the Large Helical Device (LHD). These superconductors have large cross-sectional area of high purity aluminum stabilizer to improve their stability and to enhance the overall current density. Once a normal-zone is initiated in such a composite superconductor, the current transfers to the aluminum stabilizer according to the temperature distribution. The time constant of current diffusion in the stabilizes however is very long due to the low electrical resistivity of aluminum and the large conductor size. Therefore, an excess Joule heat is generated in a small area near superconducting filaments and the temperature increases locally. In this paper, to evaluate this peculiar property, we carry out some simulations with regard to quench process in the superconductor applied to the helical coil of LHD in the National Institute for Fusion Science. The simulations, by using a newly developed computer code, are compared with the experimental results of the stability tests on the short samples of LHD conductor. Furthermore, we focus on the influence of the CuNi alloy clad adopted to the LHD conductor on the normal transition and normal-zone propagation properties.