The mid-rapidity (d sigma(pN)/d gamma at gamma = 0) and total (sigma(pN)) production cross sections of J psi mesons are measured in proton-nucleus interactions. Data collected by the HERA-B experiment in interactions of 920 GeV/c protons with carbon, titanium and tungsten targets are used for this analysis. The J psi mesons are reconstructed by their decay into lepton pairs. The total production cross section obtained is sigma(J/psi)(pN) = 663 +/- 74 +/- 46 nb/nucleon. In addition, our result is compared with previous measurements. (c) 2006 Elsevier B.V. All rights reserved.