A phenomenon in which a finite length of the normal zone propagates only to one side is observed in the helical coil of a large helical device (LHD) at the National Institute for Fusion Science. The cause of the asymmetric propagation has not yet been clarified. The LHD conductor comprises a NbTi/Cu Rutherford conductor, pure aluminum stabilizer, and copper sheath. To simulate the one-sided propagation phenomenon, a quench simulation code considering the Hall electric field generated in the aluminum and copper stabilizers was developed, and a numerical simulation was performed. One-sided propagation was successfully simulated over a wide current range, and the propagation velocity showed asymmetry even when two-sided propagation occurred. The numerically calculated propagation velocity is in good agreement with the experimental results. There is a large difference between the minimum thermal disturbance necessary for one-sided and two-sided propagation. It was concluded that the stability of the LHD helical coil was significantly degraded by the asymmetric propagation phenomenon.