A non-adiabatic nuclear wavepacket dynamics simulation of the H₂O⁺ de-excitation process is performed based on electronic structure calculations using the variational quantum eigensolver. The adiabatic potential energy surfaces and non-adiabatic coupling vectors are computed with algorithms for noisy intermediate-scale quantum devices, and time propagation is simulated with conventional methods for classical computers. The results of non-adiabatic transition dynamics from the B^~ state to A^~ state reproduce the trend reported in previous studies, which suggests that this quantum-classical hybrid scheme may be a useful application for noisy intermediate-scale quantum devices.