The cross section for coherent omega-meson photoproduction off the deuteron has been measured for the first time as a function of the momentum transfer t=(P-gamma - P-omega)(2) and photon energy E-gamma using the CLAS detector at the Thomas Jefferson National Accelerator Facility. The cross sections are measured in the energy range 1.4 < E-gamma < 3.4GeV. A model based on omega- N rescattering is consistent with the data at low and intermediate momentum transfer, vertical bar t vertical bar. For 2.8 < E-gamma < 3.4GeV, the total cross-section of omega - N scattering, based on fits within the framework of the Vector Meson Dominance model, is in the range of 30-40 mb. (C) 2018 The Authors. Published by Elsevier B.V.