We demonstrate an optically tunable mode-locked fiber laser using long-period fiber grating (LPFG) coated with multi-walled carbon nanotubes (CNTs). The multi-walled CNTs can absorb light to convert it into thermal energy, and the resonance wavelength of the grating can be easily turned by varying the external modulated light power. This multi-walled CNT coated LPFG-based all-optical fast and efficient spectrum tunable filter enables continuous tuning of the central wavelength of the laser by manipulating the loss of the mode-locked laser, ensuring the stability of the mode-locking state. In the absence of modulated light on multi-walled CNTs, the soliton laser could generate 890 fs pulses at 1546.7 nm with a spectrum bandwidth of 3.26 nm and a signal-to-noise ratio of 73.1 dB. Through adjustment of the pump power of the modulation light on multi-walled CNTs, the mode-locked fiber laser can be continuously tuned from 1546.71 to 1563.15 nm. The response time of the optically tunable system was measured to be in the order of hundreds of milliseconds. The presented optical tuning filter shows great potential in the fiber laser system, offering a repeatable, straightforward, and rapidly responsive laser tuning technique.