We perform the first search for lepton-number-violating B+ -> D(-)l(+)l'(+) decays, where l and l' stand for e or mu, using 772 x 10(6) B (B) over bar pairs accumulated at the Y(4S) resonance with the Belle detector at the KEKB e(+)e(-) collider. No evidence for these decays has been found. Assuming uniform three-body phase space distributions for the D(-)l(+)l'(+) decays, we set the following upper limits on the branching fractions at 90% confidence level.B(B+ -> D(-)e(+)e(+)) < 2.6 x 10(-6), B(B+ -> D(-)e(+mu+)) < 1.8 x 10(-6) and B(B+ -> D-mu(+)mu(+)) < 1.1 x 10(-6).