In this paper, we study the spectroscopic properties and predissociation mechanisms of 14 states, which come from the first two dissociation channels of the BF+ cation. The potential energy curves of 14 Λ-S (X2Σ+, 12Π, 22Π, 22Σ+, 14Σ+, 14Δ, 14Σ1, 12Δ, 12Σ1, 32Σ+, 14Π, 24Π, 24Σ+, and 32Π) and corresponding 30 Ω states are calculated using the complete active space self-consistent field method, which is followed by the valence internally contracted multireference configuration interaction approach with the Davidson modification. To improve the reliability and accuracy of the potential energy curves, the core-valence correlation and scalar relativistic corrections, as well as the extrapolation of potential energy to the complete basis set limit are taken into account. The spin-orbit coupling is computed using the state interaction approach with the Breit-Pauli Hamiltonian. Based on these potential energy curves, the spectroscopic parameters and vibrational levels are determined for all the bound and quasi-bound Λ-S and Ω states. The present ground-state spectroscopic constants match well with the available experimental data. In addition, the vertical and adiabatic ionization potentials from the X1Σ+ state of BF molecule to the X2Σ+, 12Π, and 22Σ+ states of BF+ cation are calculated. The results of BF+(X2Σ+) ← BF(X1Σ+) ionization are in good agreement with the measurements. Various curve crossings of Λ-S states are revealed. We calculate the spin-orbit matrix elements between two interacting electronic states in the curve crossing region. With the help of present spin-orbit coupling matrix elements, we analyze the predissociation mechanisms of X2Σ+ and 32Π states along with the perturbations of the nearby states to 22Π, 14Σ+ and 32Σ+ states for the first time. The predissociation of X2Σ+ and 32Π states have a chance to occur around the vibrational levels υ"=30 and υ'=0 due to spin-orbit coupling, respectively. The present results also indicate that the υ' ≥ 9 vibrational levels of 22Π state are perturbed by the crossing states 22Σ+, 14Σ+, 14Δ, 14Σ1, 12Δ, 12Σ1, 32Σ+, and 14Π, that the υ' ≥ 4 vibrational levels of 14Σ+ state are perturbed via the interacting states 14Σ1 and 12Σ1, and the great perturbations between υ' ≥ 4 vibrational levels of 32Σ+ state and υ' ≥ 0 vibrational levels of 14Π state. For the 30 Ω state, we also calculate the relative energies of dissociation limits compared with the lowest one matching well with the experimental ones. Finally, the Franck-Condon factors, Einstein coefficients, and radiative lifetimes are evaluated for the 22Π (υ'=0-9)-X2Σ+, 22Σ+ (υ'=0-2)-X2Σ+, (3)1/2-(1)1/21st well, and (2)3/2 (υ'=0-9)-(1)1/21st well transitions.