We have measured the thermal conductivity of methane at temperatures from 308 K down to 190.585 K, which is just 21 mK above the critical temperature, and at densities up to 14 mol L(-1). The data were obtained with an improved guarded parallel-plate eel with a new cryostat that was built especially for measurements in the critical region of methane. The new experimental data have a higher accuracy than those reported previously in the Literature and enable us to examine the validity of the currently available theoretical description of the asymptotic and nonasymptotic behavior of the thermal conductivity of fluids in the critical region. Equations for the thermal conductivity of methane in a wide range of temperatures and densities are also presented.