The amplitude versus offset/angle (AVO/AVA) inversion which recovers elastic properties of subsurface media is an essential tool in oil and gas exploration. In general, the exact Zoeppritz equation has a relatively high accuracy in modelling the reflection coefficients. However, amplitude inversion based on it is highly nonlinear, thus, requires nonlinear inversion techniques like the genetic algorithm (GA) which has been widely applied in seismology. The quantum genetic algorithm (QGA) is a variant of the GA that enjoys the advantages of quantum computing, such as qubits and superposition of states. It, however, suffers from limitations in the areas of convergence rate and escaping local minima. To address these shortcomings, in this study, we propose a hybrid quantum genetic algorithm (HQGA) that combines a self-adaptive rotating strategy, and operations of quantum mutation and catastrophe. While the self-adaptive rotating strategy improves the flexibility and efficiency of a quantum rotating gate, the operations of quantum mutation and catastrophe enhance the local and global search abilities, respectively. Using the exact Zoeppritz equation, the HQGA was applied to both synthetic and field seismic data inversion and the results were compared to those of the GA and QGA. A number of the synthetic tests show that the HQGA requires fewer searches to converge to the global solution and the inversion results have generally higher accuracy. The application to field data reveals a good agreement between the inverted parameters and real logs.