Based on first-principles calculations and symmetry arguments,we reveal that the non-centrosymmetric ternary tetradymite BiSbTe3 possesses exotic dual topological features of Weyl semimetallic phases with Z2 index (1:000).The results show that the helical Dirac-type surface states protected by the time-reversal symmetry are present in the vicinity of the Brillouin zone center,which is consistent with the experimental report.Furthermore,we show that four pairs of Weyl points reside exactly at the Fermi level,which are guaranteed to be located on high-symmetry planes due to mirror symmetries.The helical surface states and the projected Weyl nodes are well separated in the momentum space,facilitating their observations in experiments.This work not only uncovers a unique quantum phenomenon with dual topological features in the tetradymite family but also paves a fascinating avenue for exploring the coexistence of multi-topological states with wide applications.