A widely tunable mode-locked fiber laser using a carbon nanotube absorber and a fiber-optic W-shaped spectral filter is presented. The W-shaped filter is constructed by sandwiching a phase-shifted long-period grating between two LPGs of different periods. By adjusting the temperature of the W-shaped filter from 23°C to 100°C, the central wavelength of the mode-locked fiber laser can be continuously tuned from 1597 to 1553 nm. The tuning range is further extended to 1531.6 nm when a shorter erbium-doped fiber is used in the fiber oscillator. The experimental results reveal that the large thermal tunability of the proposed LPG filter provides an effective approach to achieve compact widely tunable mode-locked fiber lasers covering both C and L bands.