Potential energy curves of six electronic states (X1Σ+, a3Σ+, A1Σ+, b3Π, B1Π, c3Σ+) corresponding to the first dissociation limit Be+(2S)+X(2S) and the second dissociation limit Be+ (2P)+X(2S) of BeX+ (X=H,D,T) are calculated using the internally contracted multiconfiguration-reference configuration interaction approach based on the consistent cc-pVQZ basis set. Based on the calculated potential energy curves, one-dimensional radial Schrdinger equations are solved by using LEVEL program. Consequently, the ro-vibrational constants, Franck-Condon factors and radiative lifetimes of the corresponding electronic states are obtained. The spin-orbital coupling constants of b3Π and c3Σ+ states are respectively evaluated on the basis of the calculation of Breit-Pauli operator. The Boltzmann population distribution of A1Σ+ state of BeH+ are derived at vibrational temperatures of 2500, 5000, 7500, 10000 K. Moreover, the spectra of Δν=-2 and Δν=-3 bands in A1Σ+-X1Σ+ system at the rotational temperatures of 500, 1000, 1500, 2000 K are simulated respectively when the vibrational temperature is 10000 K.