Thermal transport in suspended graphene samples has been measured in prior works and this work with the use of a suspended electro-thermal micro-bridge method. These measurement results are analyzed here to evaluate and eliminate the errors caused by the extrinsic thermal contact resistance. It is noted that the room-temperature thermal resistance measured in a recent work increases linearly with the suspended length of the single-layer graphene samples synthesized by chemical vapor deposition (CVD), and that such a feature does not reveal the failure of Fourier’s law despite the increase in the reported apparent thermal conductivity with length. The re-analyzed apparent thermal conductivity of a single-layer CVD graphene sample reaches about 1680 ± 180 W m−1 K−1 at room temperature, which is close to the highest value reported for highly oriented pyrolytic graphite. In comparison, the apparent thermal conductivity values measured for two suspended exfoliated bi-layer graphene samples are about 880 ± 60 and 730 ± 60 Wm−1K−1 at room temperature, and approach that of the natural graphite source above room temperature. However, the low-temperature thermal conductivities of these suspended graphene samples are still considerably lower than the graphite values, with the peak thermal conductivities shifted to much higher temperatures. Analysis of the thermal conductivity data reveals that the low temperature behavior is dominated by phonon scattering by polymer residue instead of by the lateral boundary.