We investigate the growth of the Rayleigh–Taylor and Richtmyer–Meshkov instabilities at the interface of the relativistic jet using three-dimensional hydrodynamic simulations. The propagation of the relativistic jet that is continuously injected from the boundary of the calculation domain into a uniform ambient medium is solved. We find that the interface of the jet is deformed by a synergetic growth of the Rayleigh–Taylor and Richtmyer–Meshkov instabilities regardless of the launching condition, such as the specific enthalpy of the jet or the effective inertia ratio between the jet and ambient medium. The material mixing between the jet and external medium due to these instabilities causes the deceleration of the jet.