The semileptonic decays B + c → P(V) + + +ν and the nonleptonic decays B + c → P(V) + L, where P(V) denotes a pseudoscalar (vector) charmonium or (bs)-meson, and L denotes a light meson, are studied in the framework of improved instantaneous BetheSalpeter (BS) equation and the Mandelstam formula. The numerical results (width and branching ratio of the decays) are presented in tables, and in order to compare conveniently, those obtained by other approaches are also put in the relevant tables. Based on the fact that the ratio−0.040 estimated here is in good agreement with the observation by LHCb, one may conclude that with respect to the decays the present framework works quite well. B c meson, Bethe-Salpeter quark model, decay PACS number(s): 13.20.He, 13.20Fc, 13.25.Ft, 13.25.Hw, 11.10.St Citation: Chang C H, Fu H F, Wang G L, et al. Some of semileptonic and nonleptonic decays of B c meson in a Bethe-Salpeter relativistic quark model. Sci China-Phys Mech Astron, doi: 10.1007/s11433-015-5671-x B c meson carries two heavy flavor quantum numbers explicitly, and it decays only via weak interactions, although the strong and electromagnetic interactions can affect the decays.As consequences, B c meson has a comparatively long lifetime and very rich weak decay channels with sizable branching ratios. Being an explicit double heavy flavor meson, its production cross section can be estimated by perturbative QCD quite reliably and one can conclude that only via strong interaction and at hadronic high energy collisions the meson can be produced so numerously that it can be observed experimentally [1][2][3]. Therefore, the meson is specially interesting in studying its production and decays both.The first successful observation of B c was achieved *Corresponding authors (CHANG ChaoHsi, through the semileptonic decay channel B c → J/ψ + + +ν by CDF collaboration in 1998 from Run-I at Tevatron. They obtained the mass of B c : m B c = 6.40 ± 0.39 ± 0.13 GeV and the lifetime: τ B c = 0.46 +0.18 −0.16 ± 0.03 ps [4]. Later on CDF collaboration further gave a more precise mass m B c = 6275.6 ± 2.9(stat) ± 5(syst) MeV/c 2 obtained through the exclusive non-leptonic decay B c → J/ψπ + [5], and upgraded their results [6]. In the meantime D0 collaboration at Tevatron also carried out the observations and confirmed CDF results [7]. Recently LHCb reported several new observations on B c decays [8]. Thus we may reasonably expect that at LHCb in the near future the B c data will be largely enhanced and new results are issued in time.In literatures, there are many works studying various B c decays [9-28] under different approaches. Among the approaches in the market, the one used in ref. [9] is that when