The basic requirements for the grid connection of the generator motor of the gravity energy storage system are: the phase sequence, frequency, amplitude, and phase of the voltage at the generator end and the grid end must be consistent. However, in actual working conditions, there will always be errors in the voltage indicators of the generator and grid terminals, resulting in transient impulse currents. In addition, due to the difference between gravity energy storage systems and conventional power generation units, frequent switching between charging and discharging operating conditions is required according to the needs of the power grid. Each switching requires the completion of the generator motor startup and grid connection. If there is always a significant error in the voltage indicators between the generator and grid terminals during frequent grid connection, stable transient surge currents will be generated. Without human intervention, long-term operation will bring hidden dangers to the safety of the grid connected system, leading to a series of consequences such as equipment aging and even damage. In response to the above issues, this article establishes a gravity energy storage power generation/motor grid connection model. Through simulation analysis, the variation law of the weight of the impact of different terminal voltage indicators on the grid connected transient impulse current is summarized. A grid connection method for gravity energy storage systems based on sensitivity analysis of voltage grid connection indicators is proposed. Through simulation verification, this method can significantly reduce the grid connected transient impulse current while improving the success rate of grid connection, The correctness and practicality of the proposed method have been fully verified.