A novel graphene wool material was synthesised by non-catalytic chemical vapour deposition using a high-purity quartz wool substrate. The in situ synthesis method avoids post-growth transfer and isolation steps and allows the graphene to be directly synthesised into graphene wool. In the absence of a catalyst during graphene growth, the cracking of methane and nucleation is not as efficient, resulting in graphene defects which can be minimised by optimising the growth conditions. The roles of the methane and hydrogen flow rates in the synthesis of the graphene wool were investigated, as was the effect of growth temperature, growth time and cooling rates. The precursor flow rates and growth temperature were found to be the most vital parameters. The best quality graphene wool showed a minimum ratio of the disordered carbon relative to the graphitic carbon (I-D/I-G approximate to 0.8) with a calculated crystallite grain size of 24 nm. The morphology of the optimised graphene wool was flake-like, and the X-ray photoelectron spectroscopy analysis revealed a surface composition of 94.05 at.% C 1s and 5.95 at.% O 1s. With this new material, the integrity of the synthesised graphene surface is preserved in use and it has the added advantage of structural support from the quartz substrate. Unlike many other forms of graphene, this fibrous graphene wool is flexible, malleable and compressible, allowing for a wealth of potential applications including in electronics, energy storage, catalysis, and gas sorption, storage, separation and sensing applications.