  Based on first-principles calculations, we show that stoichiometric TaSe3,
synthesized in space group P21/m, belongs to a three-dimensional (3D) strong
topological insulator (TI) phase with Z2 invariants (1;100). The calculated
surface spectrum shows clearly a single Dirac cone on surfaces, with helical
spin texture at a constant energy contour. To check the stability of the
topological phase, strain effects have been systematically investigated,
showing that many topological phases survive in a wide range of the strains
along both the a- and c-axes, such as strong TI (STI), weak TI (WTI) and Dirac
semimetal phases. TaSe3 provides us an ideal platform for experimental study of
topological phase transitions. More interestingly, since superconductivity in
TaSe3 has been reported for a long time, the co-existence of topological phases
and superconducting phase suggests that TaSe3 is a realistic system to study
the interplay between topological and superconducting phases in the future.
