Stretchable supercapacitors often have laminated structures consisting of electrode, electrolyte, and supporting layers. Since the layers are likely to be composed of different materials, delamination is a major cause of failure upon stretching. In this study, we demonstrate delamination-free stretchable supercapacitors where all the component layers are prepared with a single matrix, which is composed of a polymer, poly(vinylidene fluoride-hexafluoropropylene) and an ionic liquid, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide. Since the ionic liquid in the composite plays a role as both an electrolyte and a plasticizer, this composite can be used as an electrolyte and a supporting layer in the stretchable supercapacitor. The electrode layer can be fabricated by incorporating carbon nanotubes in the common matrix. Then, all the layers can be seamlessly fused into one body by dissolving the surface of the composite with acetone, which evaporates after the integration, leaving no borders between the layers. This one-body stretchable supercapacitor not only has high durability against repetitive stretches but also is stretchable in all directions. This feature clearly distinguishes them from conventional stretchable supercapacitors fabricated using buckled structures, which are stretchable only in one or two directions. Moreover, this supercapacitor has high cell voltage (∼3 V) owing to the ionic liquid-based gel electrolytes. Our demonstration of isotropically stretchable high-durability supercapacitors may have a great implication in the development of stretchable energy storage devices for real applications.