We studied the friction coefficient between the polymer gel network and water f for thermoreversible agarose gels under various conditions of agarose concentration and gelation temperature. Since agarose gels exhibit phase separation below the gelation temperature, f strongly depends on the thermal history. We found that the friction coefficient of the phase-separated agarose gel normalized by the water viscosity, f/η, is expressed as f/η = S/ξνSD where ξSD is the frictional pore size and ν and S are constant parameters. ξSD corresponds to the correlation length of the frozen density fluctuations of the polymers via spinodal decomposition determined from small-angle light scattering. The least-squares analysis of the results shows that the exponent is ν ≃ 2 with the numerical constant of S ≃ 105/2π. The results suggest that the frictional properties of phase-separated agarose gels are dominated by the dilute regions of the bicontinuous gel structure.