<p>Non-Hermitian dynamics exhibits a wealth of surprising and potentially useful phenomena. However, it is typically realized by coupling a system with thermal reservoirs, which makes the system suffer from thermal fluctuations associated with the dissipation. Here, we propose a dissipation-free approach to realize non-Hermitian dynamics using a superconducting circuit composed of two resonators and a superconducting qutrit. The non-Hermiticity arises in the dynamical matrix for the evolution of the two resonators in the Heisenberg picture, via a photon-number non-conserved dynamics. The energy spectrum of the non-Hermitian dynamical matrix can be retrieved by measuring the state of the two resonators, and a phase transition of the energy spectrum can be observed by varying the control parameters. In the realization of the non-Hermitian dynamics, the dissipation of the system and the post-selection are not required. Thus, the approach is implemented in a deterministic way, and the reservoir-induced noise is suppressed. Numerical simulations indicate that the energy spectrum of the non-Hermitian dynamical matrix obtained via the measurement of the resonators is in accordance with the theoretical prediction. Moreover, we demonstrate the parity discrimination for the state of two four-level qudits as an application, exhibiting the potential of the non-Hermitian dynamics in the field of quantum measurement. This work opens a new avenue for the realization of non-Hermitian dynamics and may have a significant implication in exploring the non-Hermitian phenomena.</p>