The FeNiCoCr-based high entropy alloys (HEAs) exhibit excellent mechanical properties, such as twin-induced plasticity (TWIP) and phase transformation plasticity (TRIP) that can reach a remarkable combination of strength and ductility. In the present work, the face-centered-cubic (FCC) single-crystal FeNiCoCrAl0.36 HEAs were studied, using the density functional theory (DFT) combined with the phonon calculation to estimate the stacking fault energies, temperature-dependent phase stabilities of different structures. And the kinetic Monte Carlo (kMC) was used to predict the substructures evolution based on the transition state energies obtained from DFT calculations. We proposed two different formation paths of nano-twins in this Al-composited HEA and found that short-range hexagonal-close-packed (HCP)-stacking could occur in this HEA. The DFT calculations suggest that this HEA has negative stacking fault energy (SFE), HCP formation energy, and twin-formation energy at 0 K. Phonon calculations indicate that at the finite temperature, the competing FCC/HCP phase stability and propensity for twinning make it possible to form HCP-like twin boundaries. The kMC simulations suggest that under deformation, TWINs could form within the HCP laths which differs from the study of others. With the great agreement of results from kMC simulations and experiments, this twin-hcp laminated substructure formation path offers a new concept of designing TWIP HEAs containing tunable twin structures with HCP and TWIN lamellae structures, which could result in better mechanical properties of HEAs.