We study the cosmological consequences of interacting Tsallis holographic dark energy model in the framework of the fractal universe in which the Hubble radius is considered as the IR cutoff. We derive the equation of state (EoS) parameter, deceleration parameter and the evolution equation for the Tsallis holographic dark energy density parameter. Our study shows that this model can describe the current accelerating universe in both non-interacting and interacting scenarios, and also a transition occurs from the deceleration phase to the accelerated phase at the late-time. Finally, we check the compatibility of free parameters of the model with the latest observational results by using the Pantheon supernovae data, eBOSS, 6df, BOSS DR12, CMB Planck 2015, Gamma-Ray Burst.
