Using the first-principles methods, we study the formation energetics properties of intrinsic defects, and the charge doping properties of extrinsic defects in transparent conducting oxides CuCrO2. Intrinsic defects, some typical acceptortype, and donor-type extrinsic defects in their relevant charge state are considered. By systematically calculating the formation energies and transition energy, the results of calculation show that, Vcu, Oi, and Ocu are the relevant intrinsic defects in CuCrO2; among these intrinsic defects, Vcu is the most efficient acceptor in CuCrO2. It is found that all the donor-type extrinsic defects have difficulty in inducing n-conductivity in CuCrO2 because of their deep transition energy level. For all the acceptor-type extrinsic defects, substituting Mg for Cr is the most prominent doping aceeptor with relative shallow transition energy levels in CuCrO2. Our calculation results are expected to be a guide for preparing promising n-type and p-type materials in CuCrO2.