Graphene oxide (GO) was immobilized on the surfaces of acrylic yarns through a conventional dyeing approach. The GO dyed yarns and/or the fabric were immersed in an aqueous sodium hydrosulfite solution at around 363 K for 30 minutes, which converted the GO into graphene. The graphene created a graphitic-coloured and electrically conductive thin layer over each yarn in the fabric. Data on the electrical conductance of the yarns versus temperature (30K～300K) fit well with the so-called fluctuation-induced tunneling model, which suggests that the graphene layer belongs to a continuously interconnected network. Values of the electrical resistivity ranged from 10^ to 10^ Ohm/cm, as verified by the content of graphene in the conductive layer.