Orthorhombic dysprosium manganite DyMnO3 with single phase is synthesized using solid-state reaction technique and the crystal structure and dielectric properties as functions of temperature and frequency are investigated. Thermally activated dielectric relaxations are shown in the temperature dependence of the complex permittivity, and the respective peaks are found to be shifted to higher temperatures as the measuring frequency increases. In Arrhenius plots, activation energies of 0.32 and 0.24 eV for the high- and low-temperature relaxations are observed, respectively. Analysis of the relationship between the real and imaginary parts of the permittivity and the frequencies allows us to explain the dielectric behavior of DyMnO3 ceramics by the universal dielectric response model. A separation of the intrinsic grain and grain boundary properties is achieved using an equivalent circuit model. The dielectric responses of this circuit are discerned by impedance spectroscopy study. The determined grain and grain boundary effects in the orthorhombic DyMnO3 ceramics are responsible for the observed high- and low-temperature relaxations in the dielectric properties.