We use a combination of three large N-body simulations to investigate the dependence of dark matter halo concentrations on halo mass and redshift in the Wilkinson Microwave Anisotropy Probe year 5 (WMAP5) cosmology. The median relation between concentration and mass is adequately described by a power law for halo masses in the range 1011-1015h-1Msolar and redshifts z < 2, regardless of whether the halo density profiles are fitted using Navarro, Frenk & White or Einasto profiles. Compared with recent analyses of the Millennium Simulation, which uses a value of σ8 that is higher than allowed by WMAP5, z = 0 halo concentrations are reduced by factors ranging from 23 per cent at 1011h-1Msolar to 16 per cent at 1014h-1Msolar. The predicted concentrations are much lower than inferred from X-ray observations of groups and clusters.