The current paper discusses the first results of a comprehensive research project, aiming at developing a strain-hardening cementitious composite (SHCC) with self-sensing and re-centring capabilities. Superelastic shape memory alloy (SMA) can be used to provide the composite with re-centring behaviour as SMA is capable of recovering large strains. Carbon fibres are proved to be very useful for the self-sensing performance of cementitious composites. Therefore, an experimental programme was designed in the first stage of the project to investigate the effect of fibre hybridisation on the fresh, mechanical, and electrical properties of SHCC with polyvinyl alcohol (PVA) fibres. Steel fibres (SFs) were also involved in the experiments for comparison reasons. It was found that such hybridisation using SMA fibres (SMAFs) and SFs enhanced the flexural performance of composite significantly, but with a decrease in compressive characteristics of composite for some of the studied fibre contents. The electrical resistivity of SHCC with PVA fibre remained almost unchanged by the addition of SMAFs and SFs within the studied range. Furthermore, considering the type of CFs used in this study, 0.2% CFs by volume is the optimum CF content for developing a conductive SHCC without any adverse effect of CFs on the flexural performance of the composite.