We report the measurement of the thermal conductivity of a suspended single-layer graphene. The room temperature values of the thermal conductivity in the range approximately (4.84+/-0.44)x10(3) to (5.30+/-0.48)x10(3) W/mK were extracted for a single-layer graphene from the dependence of the Raman G peak frequency on the excitation laser power and independently measured G peak temperature coefficient. The extremely high value of the thermal conductivity suggests that graphene can outperform carbon nanotubes in heat conduction. The superb thermal conduction property of graphene is beneficial for the proposed electronic applications and establishes graphene as an excellent material for thermal management.