AbstractIn this work, the holographic dark energy model is constructed by using the non‐extensive nature of the Schwarzschild black hole via the Rényi entropy. Due to the non‐extensivity, the black hole can be stable under the process of fixing the non‐extensive parameter. A change undergoing such a process would then motivate us to define the energy density of the Rényi holographic dark energy (RHDE). As a result, the RHDE with choosing the characteristic length scale as the Hubble radius provides the late‐time expansion without the issue of causality. Remarkably, the proposed dark energy model contains the non‐extensive length scale parameter additional to the standard model. The cosmic evolution can be characterized by comparing the size of the Universe to this length scale. Moreover, the preferable value of the non‐extensive length scale is determined by fitting the model to recent observations. The results of this work would shed light on the interplay between the thermodynamic description of the black hole with non‐extensivity and the classical gravity description of the evolution of the Universe.