GaOx devices have been extensively explored for applications such as power devices and solar blind detectors, based on their wide bandgap. In this study, we investigated the synaptic properties of the amorphous gallium oxide (a-GaOx)- based memristor with a W/WOx/a-GaOx/ITO structure, in which a-GaOx are deposited by RF magnetic sputtering at ambient temperature. The structure and components of a-GaOx are characterized by XRD, XPS, SEM, and EDS. The electrical test indicates that W/WOx/a-GaOx is ohmic due to the thin WOx layer with a high concentration of oxygen vacancies. Consequently, the synaptic characteristics of the W/WOx/a-GaOx/ITO memristor depend on both the a-GaOx layer itself and the a-GaOx/ITO junction. The fitting results indicate that the a-GaOx/ITO junction is Schottky with unidirectional conductive properties. However, the elevated defect density results in a larger current for the reverse-biased a-GaOx/ITO junction. Moreover, adjusting the thickness of a-GaOx allows the device to achieve almost symmetrical forward and reverse currents. We have successfully observed typical synaptic characteristics in W/WOx/a-GaOx/ITO when stimulated by consecutive spike signals. Clearly, through careful design considerations regarding the structure and parameters, we have realized superior synaptic performance in a-GaOx-based memristors. This achievement shows that amorphous GaOx has great potential applications in neuromorphic computation chips for artificial intelligence or the Internet of Things in the future.