The potential energy curves of twenty-three states generated from the twelve -S states (X1+, a3, 13+, 13, 11, 11-, 13-, 21+, 11, 23, 21 and 23+) correlating with the first dissociation channel C+(2Pu)+ F(2Pu) of the CF+ cation are obtained by using the internally contracted multireference configuration interaction approach with the Davidson modification (icMRCI+Q) on the basis of the correlation-consistent aug-cc-pV5Z and aug-cc-pV6Z basis sets for the first time. The spin-orbit coupling, core-valence correlation and relativistic corrections are taken into account, and all the potential energy curves are extrapolated to the complete basis set limit by separately extrapolating the Hartree-Fock and correlation energies scheme. Based on the calculated potential energy curves, the spectroscopic parameters of the bound and quasibound nine -S and sixteen states of the CF+ cation are obtained. And the spectroscopic parameters of X1+and a31st well-S states which are in very good agreement with experimental results are achieved. Furthermore, the vertical and adiabatic ionization potentials of ionization from the X2 state of CF radical to the bound and quasibound nine -S states of the CF+ cation are calculated, and the vertical and adiabatic ionization potentials of the CF+(X1+) CF(X2 ) and CF+(a31st well) CF(X2 ) ionizations are also in good agreement with the corresponding experimental values. Various curve crossings of -S states are revealed, and with the help of our computed spin-orbit coupling matrix elements, the predissociation mechanisms of the a31st well, 111st well and 21+ states are analyzed for the first time. The spin-orbit-induced predissociations for the a31st well, 111st well and 21+-S states could happen, and the predissociations of the a31st well, 111st well and 21 +-S states start around the vibrational levels ' = 15, ' = 1 and ' = 1, respectively. Relative energies of the twenty-three states in the dissociation limits are given, and our calculations match the experimental results very well. Finally, the Franck-Condon factors and radiative lifetimes of transitions from (2) 0+1st well (;'=05), (1) 11st well ('=05) and (2) 11st well ('=0) to X0+ states are predicted for the future laboratory research.