A search is performed for the lepton number violating decay B^{+}\rightarrow h^- \mu^+ \mu^+, where h^- represents a K^- or a \pi^-, using data from the LHCb detector corresponding to an integrated luminosity of 36pb^{-1}. The decay is forbidden in the Standard Model but allowed in models with a Majorana neutrino. No signal is observed in either channel and limits of B(B^{+} \rightarrow K^- \mu^+ \mu^+) \u3c 5.4\times 10^{-8} and B(B^{+} \rightarrow \pi^- \mu^+ \mu^+) \u3c 5.8\times 10^{-8} are set at the 95% confidence level. These improve the previous best limits by factors of 40 and 30, respectively
