Abstract: A measurement of J/psi and psi(2S) production is presented. It is based on a data sample from Pb+Pb collisions at root s(NN) = 5.02 TeV and pp collisions at root s = 5.02 TeV recorded by the ATLAS detector at the LHC in 2015, corresponding to an integrated luminosity of 0.42 nb(-1) and 25 pb(-1) in Pb+Pb and pp, respectively. The measurements of per-event yields, nuclear modification factors, and non-prompt fractions are performed in the dimuon decay channel for 9 < p(T)(mu mu) < 40 GeV in dimuon transverse momentum, and -2 < y(mu mu) < 2 in rapidity. Strong suppression is found in Pb+Pb collisions for both prompt and non-prompt J/psi, increasing with event centrality. The suppression of prompt psi(2S) is observed to be stronger than that of J/psi, while the suppression of non-prompt psi(2S) is equal to that of the non-prompt J/psi within uncertainties, consistent with the expectation that both arise from b-quarks propagating through the medium. Despite prompt and non-prompt J/psi arising from different mechanisms, the dependence of their nuclear modification factors on centrality is found to be quite similar.