CCSD(T)/6-311G(2d,2p) geometry optimization and harmonic vibrational frequency computation were carried out on the X(1)A(1) state of H2Se and the X(2)B(1), A(2)A(1), and (BB2)-B-2 states of H2Se+. The B3LYP/6-311G**, B3LYP/6-311G(3df,2p), CCSD(T)/LanL2DZS++(2d,2p), and CCSD(T)/LanL2DZ++(3df,2p) calculations were also performed on the ground states of the neutral and cation. Furthermore, vertical and adiabatic ionization energies were computed at the CCSD(T)/6-311G(3df,2pd)//CCSD(T)/6-311G(2d,2p) level for the ionization processes to the three low-lying cationic states. Franck-Condon analyses and spectral simulations were then performed for the first two He I photoelectron bands of H2Se employing the ab initio data and FC procedures with the use of the harmonic oscillator approximation and the Duschinsky effect. Comparing the observed and simulated spectra as obtained at different cationic geometries, those of the two lowest-lying cationic states of H2Se+ that give the best spectral agreement are as follows : the X(2)B(1) state : r(e) = 1.471 +/- 0.001 Angstrom and theta(e) = 91.5 +/- 0.2 degrees; the A(2)A(1) state : r(e) = 1.475 +/- 0.004 Angstrom and theta(e) = 126.3 +/- 0.5 degrees.