We present predictions for gluon-fusion Higgs boson production in association with one jet at next-to-leading order in QCD. The calculation is performed retaining the full dependence on the top-quark mass. The two-loop integrals appearing in the virtual corrections are calculated numerically using the program SecDec. We show how a change of master integrals can improve the stability and runtime of the calculation. We study the Higgs boson transverse momentum distribution and compare our predictions with approximated results.