The potential energy curves of twenty-five Ω states generated from the eleven Λ-S states (X2Π, a4Σ-, A2Σ+, B2Δ, 14Π, 12Σ-, 24Π, 14Δ, 14Σ+, 22Σ- and 24Σ-) of the carbon monofluoride are calculated using the internally contracted multireference configuration interaction approach with the Davidson modification (icMRCI+Q) in the correlation-consistent aug-cc-pV5Z and aug-cc-pV6Z basis sets, for the first time so far as we know. 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 Λ-S and Ω states are obtained, and a very good agreement with experiment is achieved. It demonstrates that the spectroscopic parameters of A2Σ+(1st well), 24Π Λ-S and the eleven Ω states reported here for the first time can be expected to be reliably predicted results. The 24Π quasibound state caused by avoiding crossings are found, and the important electronic configurations of the bound and quasibound Λ-S states near the equilibrium positions Re are given. Various crossings in curves of Λ-S states are revealed, and with the help of our computed spin-orbit coupling matrix elements, the predissociation mechanisms of the a4Σ- and B2Δ states are analyzed. Dissociation relationships and dissociation channels of the twenty-five Ω states also are given. The transition properties of the A2Σ+-X2Π transitions are finally predicted, and our computed Franck-Condon factors and radiative lifetimes match the available experimental results very well.