Based on consistent basis set aug-cc-pV5Z, five low-lying potential energy curves and transition dipole moments X2∑+, A2Π, B2∑+, a4Π and b4∑+ of BD+ are calculated by using internally contracted multi-reference configuration interaction approach. According to the calculation results, ro-vibrational levels of theses electronic states are derived through solving the radial Schrödinger equation ro-vibrational equation, and then the molecular parameters, Franck-Condon factors (FCFs) and radiation life are obtained by fitting and calculations. The FCFs (f00=0.923) and radiation life for v"=0 (τ=235 ns) of A2Π-X2∑+ are suitable for achieving rapid laser cooling. Therefore, an optical-cycle for Doppler laser cooling scheme is proposed:the system includes the A2Π1/2(v'=0)-X2∑+(v"=0, 1), where the case of v'=0 contains 2 rotational levels, the cases of v"=0 and v"=1 contain 6 and 4 rotational levels, respectively. According to the proposal, we simulate the dynamic process of the molecular population in laser cooling. The BD+ can be decelerated from initial velocity of 100 m/s to 4.6 m/s (13 mK) after scattering 1150 photons during 5.4 ms.