In this work, a pioneering study on the electrical properties of composite carbon nanofibres (CNFs) using current-sensitive atomic force microscopy (CS-AFM) has been demonstrated. CNFs are highly interesting materials which are usable in a wide array of applications e.g. electrode materials for biosensors, lithium ion batteries, fuel cells and supercapacitors. CNFs offer a high specific surface area and thus have a high contact area for charge transfer. CNFs can be produced using spinnable polyacrylonitrile (PAN) as a precursor for carbonisation. For the purpose of developing efficient CNFs with high conductivity and power density, silver nanoparticle (AgNPs)-containing PAN solutions were electrospun to form composite nanofibres which was followed by heat treatment. The applied voltage of the spinning setup and the content of both PAN and the silver nanoparticles in the spinning solution were varied in order to study their influence on the morphology and the electrical properties of the nanofibres. The resultant morphologies and fibre diameters were determined by scanning electron microscopy (SEM). The formation of silver nanoparticles was characterised in solution by UV-visible absorption spectroscopy and dynamic light scattering (DLS), while energy-dispersive X-ray spectroscopy (EDX) and transmission electron microscopy (TEM) were carried out to investigate the presence as well as the average diameter of the AgNPs. The electrical properties of the CNFs were investigated using CS-AFM. This technique gives us the possibility to explore the electrical properties of single fibers and hence derive relationships between the structural features and the electrical properties. Our results show that the composite CNFs have a higher electrical conductivity than the neat CNFs and both the average diameter of the fibers and the electrical conductivity increase with an increasing AgNP content.