The electronic structures and effective masses of the N mono-doped and Al-N, Ga-N, In-N codoped ZnO system have been calculated by a first-principle method, and comparisons among different doping cases are made. According to the results, the impurity states in the codoping cases are more delocalised compared to the N mono-doping case, which means a better conductive behaviour can be obtained by codoping. Besides, compared to the Al-N and Ga-N codoping cases, the hole effective mass of In-N codoped system is much smaller, indicating the p-type conductivity can be more enhanced by In-N codoping.