The ac, dc conductivity and dielectric properties of $DyCoO_3$ were reported in the temperature range of 77 - 300K and in the frequency range of 20 Hz - 100 kHz. It was observed that at low temperature, ac conductivity is much higher than dc conductivity and the hopping carrier between localized states near the Fermi level was the dominant loss mechanism. A comparison of the measured ac conductivity $sigma(omega)$ was made with some of the models of hopping conductivity of the proposed earlier in the literature. It was observed that in $DyCoO_3$ the measured ac conductivity, over the entire frequency and temperature region, can be explained reasonably well by assuming two contributions $sigma_1(omega)$ and $sigma_2(omega)$ to the measured $sigma(omega)$. The first, $sigma_1(omega)$, which dominates at low temperature, may be due to impurity conduction in a small polaron; the second, $sigma_2(omega)$, which dominates at higher temperatures, depending on the frequency of measurements, may be due to the hopping of a small polaron and is reasonable for the dielectric relaxation peak.