Using the first-principles method, a new structure of monolayer h-CSe was predicted, exhibiting good dynamical and thermal stability. The geometrical, electronic and optical properties of monolayer h-CSe are examined at the HSE level. Furthermore, the influences of the in-plane strain and layer number on the electric properties of the two dimensional h-CSe material are studied. The results indicate that it possesses an indirect band gap, which exhibits a rich variety of behaviors depending on the small in-plane biaxial strain. The band gap of monolayer h-CSe could be easily tuned in the energy range from 0.82 eV to 2.61 eV under small in-plane biaxial strain (from -3% to 3%). Also, a band gap transition between direct and indirect types is not found. The band gap of the h-CSe materials decreases with the increase of their layer number. In addition, it was found that these h-CSe materials show excellent optical properties, including strong light harvesting ability for the ultra-violet light range of the solar spectrum. The results obtained here indicate that monolayer h-CSe may have significant potential applications in future nanoelectronic fields.