In the turbopump inducer of a liquid propellant rocket engine, cavitation is affected by acceleration that occurs during an actual launch sequence. Since cavitation instabilities such as rotating cavitations and cavitation surges are suppressed during launch, it is difficult to obtain data on the influence of acceleration on cavitation instabilities. Therefore, as a fundamental investigation, in the present study, a three-blade cyclic cascade is simulated numerically in order to investigate the influence of acceleration on time-averaged and unsteady characteristics of cavitation that arise in cascade. Several cases of acceleration in the axial direction of the cascade, including accelerations in the upstream and downstream directions, are considered. The numerical results reveal that cavity volume is suppressed in low cavitation number condition and cavitation performance increases as a result of high acceleration in the axial-downstream direction, also, the inverse tendency is observed in the axial-upstream acceleration. Then, the regions in which the individual cavitation instabilities occur shift slightly to a low-cavitation-number region as the acceleration increases downstream. In addition, in a downstream acceleration field, neither sub-synchronous rotating cavitation nor rotating-stall cavitation are observed. On the other hand, rotating-stall cavitation occurs in a relatively higher-cavitation-number region in an upstream acceleration field. Then, acceleration downstream is robust against cavitation instabilities, whereas cavitation instabilities easily occur in the case of acceleration upstream. Additionally, comparison with the Froude number under the actual launch conditions of a Japanese liquid propellant rocket reveals that the cavitation performance will not be affected by the acceleration under the current launch conditions.