A significant advance toward achieving practical applications of graphene as a two-dimensional material in nanoelectronics would be provided by successful synthesis of both n-type and p-type doped graphene. However, reliable doping and a thorough understanding of carrier transport in the presence of charged impurities governed by ionized donors or acceptors in the graphene lattice are still lacking. Here we report experimental realization of few-layer nitrogen-doped (N-doped) graphene sheets by chemical vapor deposition of organic molecule 1,3,5-triazine on Cu metal catalyst. When reducing the growth temperature, the atomic percentage of nitrogen doping is raised from 2.1% to 5.6%. With increasing doping concentration, N-doped graphene sheet exhibits a crossover from p-type to n-type behavior accompanied by a strong enhancement of electron-hole transport asymmetry, manifesting the influence of incorporated nitrogen impurities. In addition, by analyzing the data of X-ray photoelectron spectroscopy, Raman spectroscopy, and electrical measurements, we show that pyridinic and pyrrolic N impurities play an important role in determining the transport behavior of carriers in our N-doped graphene sheets.