Hawking radiation is one of the most intriguing and elusive predictions of quantum field theory in curved spacetime. Previous works simulating Hawking radiation have been mostly based on Unruh’s scenario, where the propagation of quantum field in classical gravitational background is mimicked. Here, guided by the duality between black holes in Jackiw-Teitelboim (JT) dilaton gravity and solitons in sine-Gordon (SG) field theory, we propose the use of a superconducting circuit for investigating analogue Hawking radiation. dimensional black holes can be realized as solitons of the SG equation of superconducting phase. It is found despite the absence of field theoretic dynamical modes, the analogue Hawking radiation is emitted in terms of the quantum soliton evaporation as a result of quantum perturbation of the black hole metric. Our theoretical proposal could not only facilitate the observation of relativistic quantum effects in lab, but also contribute to experimentally exploring the quantum mechanics of solitons, especially to the deep relationship between such mechanics and black hole physics.