In the perturbative QCD approach, we investigate the B(B-s) -> D-(s)((D) over bar ((s)))T and D*((s))((D) over bar*((s)))T decays, which include the Cabibbo-Kobayashi-Maskawa-favored (CKM-favored) decays and the CabibboKobayashi- Maskawa-suppressed decays, where T denotes a light tensor meson. From our calculations, we find that the nonfactorizable emission diagrams and the annihilation-type diagrams are important, especially for those color-suppressed channels. For those decays with a tensor meson emitted, the factorizable emission diagrams vanish owing to the fact that a tensor meson cannot be produced through the local (V - A) or tensor current. The numerical results show that the predictions for the branching ratios of considered charmed B decays are in the range of 10(-4) to 10(-6) for those CKM-favored decays (governed by jVcbj) and in the range of 10(-5) to 10(-8) for those CKM-suppressed decays (governed by vertical bar V-ub vertical bar). We also predict large transverse polarization contributions in many of the B(B-s) -> D*((s)) -> D*((s)) ((D) over bar ((s)) ((D) over bar*((s)))T decay channels.