Energy storage converter with vector control based on phase-locked loop (PLL) suffer instability when connecting to a weak grid. The conventional stability designs based on capacitor voltage feedforward (CVF) enhance the stability but introduce high-order integrals that significantly complicate controller parameter design. Therefore, in this paper, a stability enhancement design based on phase-locked offset is proposed to achieve the same performance and release the PLL bandwidth limitation. This superior feature enables the grid-following energy storage to operate stably in ultra-weak grids and with a superior transient response. Finally, the efficacy and validity of the proposed method is corroborated through hardware-in-the-loop tests.