Relative permeability is a critical parameter in reservoir numerical simulation and production prediction, intimately associated with reservoir architecture and fluid property. During gas injection development, substantial alterations in reservoir properties and fluid phase behavior induce dynamic changes in relative permeability. Clearly characterizing the time-varying features of relative permeability is very useful for an understanding of how gas injection influences fluid mobility within the reservoir and enhances recovery rates. In this paper, core displacement experiments are firstly conducted to obtain the characteristics of the relative permeability of oil and gas under various development stages and displacement conditions, further delineating the comprehensive shifts in reservoir properties at different gas injection stages. Subsequently, a novel reservoir numerical simulation method is proposed that considers the spatial and temporal segmentation of relative permeability curves in the reservoir simulation. Finally, a practical application is presented to clarify the effects of injection and production parameters on the development performance of gas flooding oil reservoirs. The results show the following: (i) Significant time-varying characteristics of relative permeability occur throughout gas injection development, in the early stages of gas injection, where most of the reservoir is at the gas injection front, and a rightward shift in relative oil and gas permeability indicates that gas injection promotes oil mobility. Conversely, in the later stages of gas injection, as the reservoir reaches the trailing edge of gas injection, the change trend in relative oil and gas permeability reverses, shifting leftward, thereby exacerbating the gas breakout phenomena. (ii) Increasing the rate of gas injection causes relative oil and gas permeability to move leftward, effectively enhancing the gas volume sweep coefficient and microscopic oil displacement efficiency at lower injection speeds while reducing development performance at higher injection speeds. (iii) An increase in gas injection pressure causes relative oil and gas permeability to shift rightward, and although it reduces residual oil saturation and enhances microscopic oil displacement efficiency, it also intensifies gas breakout phenomena and lowers the gas volume sweep coefficient. This paper provides theoretical guidance and technical support for the design of gas injection strategies, optimization of injection and production parameters, and production forecasting.