We report thermal conductivity (κ) measurements from 77 to 350 K on both suspended and supported few-layer graphene using a thermal-bridge configuration. The room temperature value of κ is comparable to that of bulk graphite for the largest flake, but reduces significantly for smaller flakes. The presence of a substrate lowers the value of κ, but the effect diminishes for the thermal transport in the top layers away from the substrate. For the suspended sample, the temperature dependence of κ follows a power law with an exponent of 1.4 ± 0.1, suggesting that the flexural phonon modes contribute significantly to the thermal transport of the suspended graphene. The measured values of κ are generally lower than those from theoretical studies. We attribute this deviation to the phonon-boundary scattering at the graphene-contact interfaces, which is shown to significantly reduce the apparent measured thermal conductance of graphene.