This paper introduces an all-optical tuning scheme of multi-walled carbon nanotubes (MWCNT) coated microcavity, achieving across the free spectral range (FSR), high-speed, precise resonance control. A modulation laser input through the microcavity tail fiber adjusts the resonance peak position, achieving a tuning efficiency of 107.3 pm/mW below 15 mW, with a maximum range exceeding one FSR and a response time of ~20 ms. Combined with a fixed-wavelength pump, this scheme can precisely control the microcomb states. The scheme offers high tuning efficiency, simple fabrication, and low cost, making it suitable for applications in microcomb control and optical filters.