The thermal conductivity (κ) and thermoelectric power (S) of the PrBa2Cu4O8 compound have been studied as a function of temperature. The κ value of the metallic PrBa2Cu4O8 compound remains nearly constant down to ∼50 K while that of the semiconducting PrBa2Cu3O7-x compound shows a monotonical decrease over a wide temperature range. The S(T) value of the PrBa2Cu4O8 sample decreases rapidly below 150 K and then reaches a small value of ∼1 µ V/K. These behaviors in κ(T) and S(T) for the metallic PrBa2Cu4O8 compound are qualitatively different from those for the semiconducting PrBa2Cu3O7-x compound, which is probably related to the charge carrier conduction along the double CuO chains. These experimental results of κ and S support a dimensional crossover of electronic transport from a 1-dimensional conduction along the CuO chain to a quasi-2 dimensional one, which results in a bandlike conduction not only along the CuO chain but also between the CuO chains.