Numerical simulations were carried out on the transient stability of large-scale composite superconductors against a thermal disturbance, that is, a LHD conductor, which consists of a NbTi/Cu Rutherford cable, a pure aluminum stabilizer, and a copper sheath around the composite. The simulations were also performed on an Al-less test conductor, which is a LHD conductor without the Al stabilizer and a half of the copper sheath. The recovery and propagation characteristics of an initiated normal zone were simulated to know the effect of the Al stabilizer on the transient stability of the LHD conductor cooled by Liq.He II. The normal zone propagation initiating current at a certain magnetic flux density for the LHD conductor was compared with that for the Al-less test conductor. Asymmetrical propagation of the normal zone appears even in the LHD based conductor without the Al stabilizer. The range of the transport current, which lead to the one-side propagation, is narrower than those for the LHD conductor. It is confirmed that the Al stabilizer in LHD conductor plays main role in the asymmetrical normal zone propagation. The high performance of the He II cooling in the transient state for the Al-less test conductor makes the normal zone initiating current up to the same level of that for the super-stabilized LHD conductor. It is confirmed that only a slight area of the thick aluminum works as a stabilizer at the transient state because of its low magnetic diffusion factor. © 2007 IEEE.