A Gaussian wave function is used for detailed study of mass spectra of the B and BS mesons using a Cornell potential incorporated with a O(1/m) correction in the potential energy term and expansion of the kinetic energy term up to a O p 10 for relativistic correction of the Hamiltonian. The predicted excited states for the B and Bs mesons are in very good agreement with results obtained by experiment. We assigned the B2(5747) and Bs2(5840) as 1 3 p2 state, the B1(5721) and Bs1(5830) as 1p1 state, the B0(5732) as 1 3 p0 state, the Bs1(5850) as 1p 1 state and the B(5970) as 2 3 S1 state. We investigate the Regge trajectories in the (J, M 2 ) and (nr, M 2 ) planes with their corresponding parameters. Branching ratio for leptonic and radiative-leptonic decays are estimated for the B and BS mesons. Our results are in good agreement with experimental observation as well as outcomes of other theoretical models.Chinese Physics C Vol. xx, No. x (201x) xxxxxx cay widths.Results of mass spectra, leptonic and radiative-leptonic decays are discussed in Section 3. In Section 3.1, we investigate Regge trajectories in the (J, M 2 ) and (n r , M 2 ) planes. Finally, we present the conclusion in Section 4.