We calculate the two-body strong decays of the orbitally excited scalar mesons D_0^*(2400) and D_J^*(3000) by using the relativistic Bethe–Salpeter (BS) method. D_J^*(3000) was observed recently by the LHCb Collaboration, the quantum number of which has not been determined yet. In this paper, we assume that it is the 0^+(2P) state and obtain the transition amplitude by using the PCAC relation, low-energy theorem and effective Lagrangian method. For the 1P state, the total widths of D_0^*(2400)^{0} and D_0^*(2400)^+ are 226 and 246 MeV, respectively. With the assumption of 0^+(2P) state, the widths of D_J^*(3000)^0 and D_J^*(3000)^+ are both about 131 MeV, which is close to the present experimental data. Therefore, D_J^*(3000) is a strong candidate for the 2^3P_0 state.