Using the newly measured masses of B c (1S ) and B c (2S ) from the CMS Collaboration and the 1S hyperfine splitting determined from the lattice QCD as constrains, we calculate the B c mass spectrum up to the 6S multiplet with a nonrelativistic linear potential model. Furthermore, using the wave functions from this model we calculate the radiative transitions between the B c states within a constituent quark model. For the higher mass B c states lying above DB threshold, we also evaluate the Okubo-Zweig-Iizuka (OZI) allowed two-body strong decays with the 3 P 0 model. Our study indicates that besides there are large potentials for the observations of the low-lying B c states below the DB threshold via their radiative transitions, some higher mass B c states, such as B c (2 3 P 2 ), B c (2 3 D 1 ), B c (3 3 D 1 ), B c (4 3 P 0 ), and the 1F-wave B c states, might be first observed in their dominant strong decay channels DB, DB * or D * B at the LHC for their relatively narrow widths.PACS numbers: