Functionalization of carbon nanotubes (CNTs) is essential for the dispersion of CNTs in polymer matrices due to their inherence. However, conventional functional groups are insulating in nature, thereby destroying the basic structure of the CNTs and their electrical conductivity due to the harsh and long-period acid treatments. Hence, a new method of functionalization is essential. In this article, a poly(vinyliedene fluoride) (PVDF) composite comprising graphene wrapped CNTs as a conducting filler is described. A strain-gauge factor of ≈20 at low strain levels (0.1%) is with a 3 wt% graphene wrapped CNT hybrid in PVDF, which overwhelms conventional metal foil strain gauges as well as functionalized CNT or functionalized graphene based polymer composites for strain sensing. A unique type of graphene wrapping over carbon nanotubes (CNTs) is achieved by chemical vapour deposition (CVD) and the same is used to prepare polymer nanocomposite films. A better and high strain gauge factor of ≈20 is obtained with conducting graphene wrapped CNTs based PVDF composites whereas the gauge factor is ≈2 with OH/COOH-CNT based PVDF composites. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.