Several low-lying electronic states of GeSe up to the energy of 36 000 cm(-1) have been studied by using the ab initio-based multireference singles and doubles configuration interaction calculations which include relativistic effective core potentials. Potential energy curves of 18 Lambda-S states which dissociate into the ground-state limit Ge(P-3(g))+Se(P-3(g)) have been computed. Effects of spin-orbit coupling on these states are also studied. We have also computed potential energy curves of bound Omega-states arising from those 18 Lambda-S states within the energy limit of 31 000 cm(-1). Spectroscopic constants (r(e), T-e, omega(e), and beta(e)) at equilibrium of all bound states are estimated. The ground state of GeSe is XO+ ((1) Sigma(+)) originating mainly from sigma(2) sigma(2) sigma(2) pi(4) and sigma(2) sigma(2) sigma(2) pi(3) pi configurations with r(e) = 2.172 Angstrom, omega(e) = 382 cm(-1), and beta(e) = 0.093 cm(-1). The agreements with the available experimental values are fairly good. The spin-orbit interactions have little effects on the composition of the low-lying states. The transition energy of the observed A(1)((1) Pi) <-- XO+ ((1) Sigma(+)) transition agrees well with the calculated value. The Lifetimes of the excited A(1) Pi and 2(1) Sigma(+) states are estimated to be 0.42 and 0.45 mu s, respectively.