Abstract: This paper reports the first differential measurement of the charged-current interaction cross section of nu(mu) on water with no pions in the final state. This flux-averaged measurement has been made using the T2K experiment's off-axis near detector, and is reported in doubly differential bins of muon momentum and angle. The flux-averaged total cross section in a restricted region of phase space was found to be sigma = (0.95 +/- 0.08(stat) +/- 0.06(det syst) +/- 0.04(model syst) +/- 0.08(flux)) x 10(-38) cm(2)/n.