The d.c. electrical conductivity along c- and a, b-axes for the Bi2CuO4 single crystal has been studied as a function of temperature for the first time. We have observed that the variable range hopping mechanism can not dominate the charge transport process in Bi2CuO4, unlike the rare earth cuprate La2CuO4. On the contrary, we have observed that the temperature dependence of the d.c. conductivity s can be described by s ~ Tp, where the exponent p is dependent on the measurement axes and on the temperature range. We have interpreted the results in the framework of the multiphonon assisted hopping theory with a weak electron-phonon coupling.