We report an experimental investigation of the edge effect on the room-temperature transport in graphene nanoribbon and graphene sheet (both single-layer and bilayer). By measuring the resistance scaling behaviors at both low- and high-carrier densities, we show that the transport of single-layer nanoribbons lies in a strong localization regime, which can be attributed to an edge effect. We find that this edge effect can be weakened by enlarging the width, decreasing the carrier densities, or adding an extra layer. From graphene nanoribbon to graphene sheet, the data show a dimensional crossover of the transport regimes possibly due to the drastic change of the edge effect.