Growth of carbon nanotubes (CNTs) onto the fibre surface by direct chemical vapour deposition (CVD) offers a convenient means to integrate synthesis with assembly. This method delivers the nanostructures where they have the greatest influence on fibre-matrix interface or interphase. However, CVD is usually limited to small batches of short fibre lengths, and can damage the primary properties. Here, we describe a robust process to produce carbon nanotube-grafted-fibres continuously at tow level with a uniform coverage of short (sub-500 nm length), 10-20 nm diameter CNTs. Different CNT growth conditions, such as temperature [650-950 °C], duration [0.72-50 min], line speed [0.6-10 m/h], potential difference [0-1000 V], and reactive gas flow/compositions were investigated. Following optimisation, the fabrication of an entirely “fuzzy” fibre reinforced hierarchical composite was achieved.