We report the result for a search for the leptonic decay of B+ -> mu(+)nu mu using the full Belle dataset of 711 fb(-1) of integrated luminosity at the gamma(4S) resonance. In the Standard Model leptonic B-meson decays are helicity and Cabibbo-Kobayashi-Maskawa suppressed. To maximize sensitivity an inclusive tagging approach is used to reconstruct the second B meson produced in the collision. The directional information from this second B meson is used to boost the observed mu into the signal B-meson rest frame, in which the mu has a monochromatic momentum spectrum. Though its momentum is smeared by the experimental resolution, this technique improves the analysis sensitivity considerably. Analyzing the mu momentum spectrum in this frame we find B(B+ -> mu(+)nu mu)=(5.3 +/- 2.0 +/- 0.9) x 10(-7) with a one-sided significance of 2.8 standard deviations over the background-only hypothesis. This translates to a frequentist upper limit of B(B+ -> mu(+)nu mu) < 8.6 x 10(-7) at 90% confidence level. The experimental spectrum is then used to search for a massive sterile neutrino, B+ -> mu N+, but no evidence is observed for a sterile neutrino with a mass in a range of 01.5 GeV. The determined B+ -> mu(+)nu mu branching fraction limit is further used to constrain the mass and coupling space of the type II and type III two-Higgs-doublet models.