We study the production of W bosons at large transverse momentum in pp collisions at the CERN Large Hadron Collider. We calculate the complete next-to-leading order (NLO) corrections to the differential cross section. We find that the NLO corrections provide a large increase to the cross section but, surprisingly, do not reduce the scale dependence relative to leading order (LO). We also calculate next-to-next-to-leading-order (NNLO) soft-gluon corrections and find that, although they are small, they significantly reduce the scale dependence thus providing a more stable result.