We report a study of the decays B -> D-s1(2536)+ (D) over bar (()()), where (D) over bar (()()) is (D) over bar (0), D- or D*(-), using a sample of 657 x 10(6)B (B) over bar pairs collected at the Y(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. The branching fractions of the decays B+ -> D-s1(2536)(+) (D) over bar (0), B-0 -> D-s1(2536)D-+(-) and B-0 -> D-s1(2536)D+(-) multiplied by that of D-s1(2536)(+) -> (DK-0(+) + DK-+(0)) are found to be (3.97 +/- 0.85 +/- 0.56) x 10(-4), (2.75 +/- 0.62 +/- 0.36) x 10(-4) and (5.01 +/- 1.21 +/- 0.70) x 10(-4), respectively. The ratio B(D-s1 -> DK-0(+))/B(D-s1 -> D*K-+(0)) is measured to be 0.88 +/- 0.24 +/- 0.08.