The electron paramagnetic resonance (EPR) studies of Re3+ (RE = Nd, Gd, Dy) doped CdMoO4 single crystals grown by Czochralski method were carried out in 4-300 K temperature range. Analysis of EPR spectra lineshapes and resonance field dependence on crystal orientation in an external magnetic field allowed allocate the Re3+ ions to the low symmetry site of Cd2+ in CdMoO4 crystal. Additionally, RE3+ complex magnetic entities created due to charge compensation, were registered. In the case of Nd3+ doped CdMoO4 crystal the values of g spectroscopic matrix were calculated and the influence of the excited states via the Orbach process was observed.