The potential energy curves of the low-lying electronic states of BeH+ molecular ion are performed by using highly accurate multi-reference configuration interaction with AV5Z basis sets for H atom and ACV5Z basis set for Be atom, 1s inner shell of Be is considered as the core orbit and the active orbit, respectively, which are used to characterise the spectroscopic properties of a manifold of singlet and triplet states. Fourteen electronic states correlated with eight dissociation channels are investigated, we have found that the a3Σ+ and c3Σ+ both are bound states, the 33Σ+ possesses double wells, and the C1Σ+, 33Σ+, 23Π, 21Π, 11Δ, 13Δ, 23Δ and 21Δ states are studied for the first time. Transition dipole moment, Franck–Condon factors qυ′υ″ and Einstein coefficients Aυ′υ″ for A1Σ+–X1Σ+, 21Π–B1Π, c3Σ+–a3Σ+ and b3Π–a3Σ+ systems have been calculated. Radiative lifetime of A1Σ+–X1Σ+ band system has also been determined.