The discovery of the unprecedented figure of merit ZT of SnSe has sparked a large number of studies on the fundamental physics of this material and further improvement through guided materials design and optimization. Motivated by its rich chemical bonding characters, unusual multi-valley electronic structure, and the sensitivity of the band edge states to lattice strains, we carry out accurate quasiparticle calculations for the low temperature phase SnSe under strains. We illustrate how the band edge states can be engineered by lattice strains, including the size and the nature of the band gap, the positions of the band extrema in the Brillouin zone, and the control of the number of electron and/or hole valleys. The distinct atomic origin and orientation of the wave functions of the different band edge states dictates the relative shift in their band energy, enabling active control of the near-edge electronic structure of this material. Our work demonstrates that strain engineering is a promising way to manipulate the low-energy electronic structure of SnSe, which can have profound influences on the optical and transport properties of this material.2