Using ab initio electronic structure calculations we investigate the change of the band structure and the nu_0 topological invariant in HgSe (non-centrosymmetric system) under two different type of uniaxial strain along the [001] and [110] directions, respectively. Both compressive [001] and [110] strain leads to the opening of a (crystal field) band gap (with a maximum value of about 37 meV) in the vicinity of Gamma, and the concomitant formation of a camel-back- (inverse camel-back-) shape valence (conduction) band along the direction perpendicular to the strain with a minimum (maximum) at Gamma. We find that the Z_2 invariant nu_0=1, which demonstrates conclusively that HgSe is a strong topological insulator (TI). With further increase of the strain the band gap decreases vanishing at a critical strain value (which depends on the strain type) where HgSe undergoes a transition from a strong TI to a trivial (normal) insulator. HgSe exhibits a similar behavior under a tensile [110] uniaxial strain. On the other hand, HgSe remains a normal insulator by applying a [001] tensile uniaxial strain. Complementary electronic structure calculations of the non-polar (110) surface under compressive [110] tensile strain show two Dirac cones at the Gamma point whose spin chiral states are associated with the top and bottom slab surfaces. ; Comment: 8 pages, 8 figures