The N incorporation effect in Hf-based high-k gate dielectrics has been studied by the first-principles calculations. Interactions between N atoms and oxygen vacancies (Vos) in HfO2 are investigated. Our calculations show that N atoms favorably occupy nearest neighbor oxygen sites to Vos. As a result, electron charge traps at Vos are remarkably suppressed due to the strong repulsive Coulomb interactions between electrons and negatively charged N 3- ions. These results indicate that N incorporation improves positive bias temperature instability (PBTI) in Hf related high-k gate stacks. Moreover, our calculations have also revealed that the Vo formation energy is remarkably reduced by N incorporation.