We consider the zero frequency electrical and the thermal conductivity of the disordered one-dimensional quantum sine-Gordon system (g 2 = 4π) with use of a Fermi-Bose relation and a self-consistent t matrix approximation. Two types of impurities are discussed. We find that the behavior of the @'Lorenz@' number is very different from the other when the gap energy ω g is finite. At low temperatures one type of impurities gives the @'Lorenz@' number α~(ω g / T ) 2 , while the other one gives α~2.