Measurement of diffractive dijet production with ZEUS at HERA Diffractive dijet production was measured with the ZEUS detector at HERA using an integrated luminosity of 61 pb^-1. The data cover virtualities of the exchanged virtual photon of 5 < Q2 < 100 GeV2 and gamma* p centre-of-mass energies of 100 < W < 250 GeV. The jets, identified using the inclusive k_T algorithm in the gamma* p frame, were required to have a transverse energy E*_T > 4 GeV. The jet with the highest transverse energy was required to have E*_T > 5 GeV. All jets were required to be in the pseudorapidity range -3.5 < eta*_jet <0. The differential cross sections are compared to leading-order predictions and next-to-leading-order QCD calculations based on recent diffractive parton densities extracted from inclusive diffractive deep inelastic scattering data.