The strength of the distribution network decreases with the integration of renewable energy sources (RESs), which leads to worse power and voltage fluctuation. The storage can suppress the power and frequency disturbance. Especially, when operated in the grid-forming (GFM) mode, the storage inverter can further support the voltage and frequency of the weak grid. However, in this mode, even a minor frequency deviation will cause a power change in the storage inverter, which significantly decreases the lifespan of storage. This problem is traditionally solved by the frequency deadband, where it is difficult to set in GFM control storage. To solve this problem, an improved GFM control for storage inverters is proposed to achieve deadband control in the voltage mode. A transfer function model of primary frequency regulation considering the mechanical delay of synchronous generators (SGs) with GFM control storage is established, which is used for theoretical analysis of improving frequency performance of weak power grid. Then, a control strategy of improving the power-frequency (p-f) droop loop is proposed to achieve the frequency deadband for storage with GFM control. Finally, the results verify the effectiveness of decreasing the action times of SG’s governor, prohibiting storage charging and discharging with small frequency disturbance through setting an appropriate deadband for storage, which can extend the lifespan of storage and SG’s governor.