In the present work, a theoretical investigation for 19 low-lying electronic states, by using ab initio method, for low-lying electronic states of the molecule HgSe in the representation has been performed via CASSCF/MRCI method (single and double excitations with Davidson corrections by using Gaussian basis set). Calculations have been performed via computational physics program MOLPRO taking the advantage of the graphical user interface GABEDIT. The potential energy curves, the electronic energy with respect to the ground state energy Te, the harmonic frequency e, and the internuclear distance re have been calculated along with the rotational constant Be. The comparison of the present result of the ground state X3with the available theoretical value in literature show an overall very good agreement. To the best of our knowledge, new states have been investigated for the first time through this work.