We report on the measurements of nonlinear current-voltage characteristics of graphene fabricated by chemical vapor deposition.The current-voltage characteristic is described by a power law with a superlinear dependence of the current on the voltage,and the nonlinearity depends on the carrier density and the excitation level.The nonlinearity is strongest at the Dirac point and becomes weaker as the carrier density increases.At the Dirac point,we also observe a crossover to a much stronger nonlinear transport when the electric field increases above 104 V/m.