Cellulose fibers were carbonized at 900 °C to make fiber networks having conducting properties. Dynamic viscoelasticity and electrical conductivity of the conductive fiber networks were examined. The storage modulus, G', of the networks increased with the network concentration, c, and a power law was found between G' and c: G' = kc^α. The exponent, α, was almost the same as that of the other power law for non-carbonized cellulose fiber networks. The electrical conductivity, σ, of the conductive fiber networks also increased with c, and another power law was found between σ and c: σ = k'c^β. The value of exponent, β, was almost the same as α. The coincidence of the exponents for the power law relationships indicates that both of the viscoelastic and electric behaviors of the networks were expressed with the same formula attributed to transfer phenomena, that is momentum and electron transfer, respectively.