A dynamic transient flow analysis method considering complex factors such as the cyclic injection and production history in a gas field storage facility was established in view of the limitations of the existing methods for transient flow analysis and the characteristics of the injection-production operation of strongly heterogeneous gas reservoirs, and the corresponding theoretical charts were drawn. In addition, an injection-production dynamic transient flow analysis model named "three points and two stages" suitable for an underground gas storage (UGS) well with alternate working conditions was proposed. The "three points" refer to three time points during cyclic injection and production, namely, the starting point of gas injection for UGS construction, the beginning and ending points of the injection-production analysis stage; and the "two stages" refer to historical flow stage and injection-production analysis stage. The study shows that the dimensionless pseudo-pressure and dimensionless pseudo-pressure integral curves of UGS well flex downward in the early stage of the injection and production process, and the dimensionless pseudo-pressure integral derivative curve is convex during the gas production period and concave during the gas injection period, and the curves under different flow histories have atypical features. The new method present in this paper can analyze transient flow of UGS accurately. The application of this method to typical wells in Hutubi gas storage shows that the new method can fit the pressure history accurately, and obtain reliable parameters and results.