Conventional sliding-mode observer (SMO)-based grid-voltage observation methods often require a low-pass filter (LPF) to remove high-frequency sliding-mode noise. However, a complicated phase- and amplitude-compensation method, which is highly sensitive to the DC-offset, is required. A frequency-adaptive dual second-order generalized integrator (SOGI) can be used to replace the LPF, eliminating the compensation link and the effects of the DC-offset; however, strong coupling is introduced between the front-end SOGI block and back-end phase-locked loop (PLL) block, thereby reducing the dynamic performance. To solve this problem, this study proposes an SMO-based grid-voltage observation method with a frequency-fixed dual SOGI and cross-compensated PLL that can eliminate the frequency coupling between the front-end SOGI block and back-end PLL blocks, thereby increasing its dynamic performance. In this study, the phase and amplitude are compensated simultaneously using the proposed cross-compensation method, achieving an accurate observation of the grid voltage under off-nominal frequencies. An analysis of the small-signal model theoretically verified that the proposed method has good dynamic performance. Finally, the superiority of the proposed method is verified through comparative experiments.