Topological insulators are characterized by Z(2) indices, and their metallic surface states are protected by time-reversal symmetry. In topological crystalline insulators, on the other hand, crystal symmetry plays a key role in protecting surface states. Therefore, perturbation breaking time-reversal or crystal symmetry induces a phase transition to a conventional band insulator. In dual topological insulators (DTIs), in which time-reversal and crystal symmetries coexist, the topological character is more robust against perturbation. Here, we propose that NaZnBi is a new DTI with Z(2) invariants (nu(0); nu(1)nu(2)nu(3)) = (1; 000) and odd mirror Chern numbers +/- 1. We find that the characteristic Dirac cone is preserved even if either time-reversal or mirror symmetry is broken, verifying the robustness of the DTI phase. Given that gapless surface states can be experimentally observable even under perturbations that break any lattice symmetry or time-reversal, NaZnBi can be a good candidate material for future device applications.