This study describes the preparation and electrical characterisation of conducting carbon black-filled/styrene-butadiene-styrene tri-block copolymer. Composites containing 5 and 10 vol% of carbon black were studied. The carbon black distribution, conductive mechanism and electrical properties of the composites were investigated from 8 to 304 K. For the first time, an analysis of the differential activation energy is carried out for carbon black composites, allowing the classification of the variable range hopping as one-dimensional for composite containing 5% of carbon black and as three-dimensional for the composite containing 10% of carbon black. Such results are found to be determined by two factors: the concentration of carbon black in the filler-rich phase and by the structural continuity of this phase. Increasing the carbon black content induces structural transition that results in variable range hopping conduction changing from one-dimensional to three-dimensional. From the hopping parameters, the mean hopping distance, the density of active centres and the energy associated with it were obtained.