We have searched for the lepton-number violating processes B^+→h^-ℓ^+ℓ^+ with h^-=K^-/π^- and ℓ^+=e^+/μ^+, using a sample of 471±3 million BB̅ events collected with the BABAR detector at the PEP-II e^+e^- collider at the SLAC National Accelerator Laboratory. We find no evidence for these decays and place 90%-confidence-level upper limits on their branching fractions B(B^+→π^-e^+e^+)<2.3×10^(-8), B(B^+→K^-e^+e^+)<3.0×10^(-8), B(B^+→π^-μ^+μ^+)<10.7×10^(-8), and B(B^+→K^-μ^+μ^+)<6.7×10^(-8)
