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) → (P, V, S, A) ν , 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 B → P and V modes have been measured very well in experiment and our theoretical values are in good agreement with them. The ones for B → 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 B → D * 0 (2400) ν and B s → D * − s0 (2317) ν as (2.31 ± 0.25) × 10 −3 and (3.07±0.34)×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.