Tissue-specific self-assembling peptide (SAP) hydrogels designed based on biologically relevant peptide sequences have great potential in regenerative medicine. These materials spontaneously form 3D networks of physically assembled nanofibres utilising non-covalent interactions. The nanofibrous structure of SAPs is often compared to that of electrospun scaffolds. These electrospun nanofibers are produced as sheets that can be engineered from a variety of polymers that can be chemically modified to incorporate many molecules including drugs and growth factors. However, their macroscale morphology limits them to wrapping and bandaging applications. Here, for the first time, we combine the benefits of these systems to describe a two-component composite scaffold from these biomaterials, with the design goal of providing a hydrogel scaffold that presents 3D structures, and also has temporal control over drug delivery. Short fibres, cut from electrospun scaffolds, were mixed with our tissue-specific SAP hydrogel to provide a range of nanofibre sizes found in the extracellular matrix (10-300 nm in diameter). The composite material maintained the shear-thinning and void-filling properties of SAP hydrogels that have previously been shown to be effective for minimally invasive material injection, cell delivery and subsequent in vivo integration. Both scaffold components were separately loaded with growth factors, important signaling molecules in tissue regeneration whose rapid degradation limits their clinical efficacy. The two biomaterials provided sequential growth factor delivery profiles: the SAP hydrogel provided a burst release, with the release rate decreasing over 12 hours, while the electrospun nanofibres provided a more constant, sustained delivery. Importantly, this second release commenced 6 days later. The design rules established here to provide temporally distinct release profiles can enable researchers to target specific stages in regeneration, such as the acute immune response versus sustained protection and survival of cells following injury. In summary, this novel composite material combines the physical advantages of SAP hydrogels and electrospun nanofibres, while additionally providing a superior vehicle for the stabilisation and controlled delivery of growth factors necessary for optimal tissue repair.