We report our theoretical calculations on the branching fractions for the semileptonic B and B_s decays based on the form factors in the covariant light-front quark model. That is, B (B_s) rightarrow (P,, V,, S,,A) ell nu _ell , where P and V denote the pseudoscalar and vector mesons, respectively, while S denotes the scalar meson with mass above 1 GeV and A the axial-vector meson. The branching fractions for the semileptonic Brightarrow P and V modes have been measured very well in experiment and our theoretical values are in good agreement with them. The ones for Brightarrow S and A modes are our theoretical predictions. There is little experimental information on the semileptonic B_s decays although much theoretical effort has been done. In addition, we predict the branching fractions of Brightarrow D^*_0(2400) ell bar{nu }_ell and B_srightarrow D^{*-}_{s0}(2317) ell bar{nu }_ell as (2.31pm 0.25)times 10^{-3} and (3.07pm 0.34)times 10^{-3}, in order, assuming them as the conventional mesons with quark-antiquark configuration. The high luminosity e^+e^- collider SuperKEKB/Belle-II is running, with the data sample enhanced by a factor of 40 compared to Belle, which will provide huge opportunity for the test of the theoretical predictions and further help understand the inner structure of these scalar and axial-vector mesons, e.g., the glueball content of f_0(1710) and the mixing angles for the axial-vector mesons. These decay channels can also be accessed by the LHCb experiment.