Potential energy curves of dipole moments for 12 electronic states correlating with the Se⁺(⁴Su) + H(²Sg), Se⁺(²Du) + H(²Sg) and Se⁺(²Pu) + H(²Sg) dissociation channels of SeH⁺ anion are calculated by the ic-MRCI + Q method. The AV5Z-DK basis set for Se atom and H atom are chosen. Scalar relativistic effect, core-valence correction, and spin-orbit coupling effect are also taken into account. In MRCI calculations, Se(1s2s) orbitals are frozen, H(1s) and Se(4s4p) orbitals are selected as active space, and the remaining orbitals are used for the core-valence correlation. Spectroscopic parameters of 12 Λ–S states and 9 low-lying Ω states are obtained. All Λ–S states we selected are bound states. The X³Σ^–, a¹Δ, b¹Σ⁺, A³Π and c¹Π states each possess a large well, but the others each have a shallow well. The a¹Δ, b¹Σ⁺, A³Π, c¹Π and 1⁵Σ^– states cross in 30000–40000 cm^–1 regions. The X³Σ^–, a¹Δ and b¹Σ⁺ come from the 4π² electronic configuration around the equilibrium region, and three states have similar values of R_e. The splitting dissociation channels are obtained at a spin-orbital coupling level. The calculated energy differences among five dissociation channels are in excellent agreement with the experimental data, and the maximal error is smaller than 0.5%. Due to the avoided crossing between the low-lying Ω states, the a2, b0⁺, A₁2, A₂1, A₃0^–, A₄0⁺ and c1 states all have two wells. The splitting parameters A^SO of the X³Σ^– state and the A³Π state are predicted at the same time, i. e. A^SO(X₂1 – X₁0⁺) = 252.4 cm^–1, A^SO(A₂1 – A₁2) = 858.9 cm^–1, A^SO(A₃0^– – A₂1) = 1213.5 cm^–1 and A^SO(A₄0⁺ – A₃0^–) = 199.5 cm^–1. The transition dipole moments of the A³Π $ \leftrightarrow $ X³Σ^– and A₂1 $ \leftrightarrow $ X₁0⁺ transitions are obtained. The oscillator strengths, Franck-Condon factors, and radiative lifetimes of these two transitions are also predicted. The radiative lifetime of A³Π state and A₂1 state are 746.6 and 787.8 ns, respectively. It implies the ability of electron transition for these two transitions.