In this study we have prepared a tubular knitted scaffold from a 9 ply multiwalled carbon nanotube (MWCNT) yarn and a composite scaffold, formed by electrospinning poly(lactic-co-glycolic acid) (PLGA) nanofibres onto the knitted scaffold. Both structures were assessed for in vitro biocompatibility with NR6 mouse fibroblast cells for up to 22 days and their suitability as tissue engineering scaffolds considered. The MWCNT yarn was found to support cell growth throughout the culture period, with fibroblasts attaching to, and proliferating on, the yarn surface. The knitted tubular scaffold contained large pores that inhibited cell spanning, leading to the formation of cell clusters on the yarn, and an uneven cell distribution on the scaffold surface. The smaller pores, created through electrospinning, were found to promote cell spanning, leading to a uniform distribution of cells on the composite scaffold surface. Evaluation of the electrical and mechanical properties of the knitted scaffold determined resistance levels of 0.9 kOmega/cm, with a breaking load and extension to break approaching 0.7N and 8%, respectively. The PLGA/MWCNT composite scaffold presented in this work not only supports cell growth, but also has the potential to utilize the full range of electrical and mechanical properties that carbon nanotubes have to offer.