A widely tunable microwave photonic notch filter with adjustable bandwidth based on multi-wavelength fiber laser is proposed and demonstrated. The multi-wavelength fiber laser generates the multi-taps of the microwave photonic filter (MPF). In order to obtain notch frequency response, a Fourier-domain optical processor (FD-OP) is introduced to control the amplitude and phase of the optical carrier and phase modulation sidebands. By adjusting the polarization controller (PC), different numbers of taps are got, such as 6, 8, 10 and 12. And the wavelength spacing of the multi-wavelength laser is 0.4 nm. The bandwidth of the notch filter is changed by adjusting the number of taps and the corresponding bandwidths are 4.41 GHz, 3.30 GHz, 2.64 GHz and 2.19 GHz, respectively. With the additional phase shift introduced by FD-OP, the notch position is continuously tuned in the whole free spectral range (FSR) of 27.94 GHz. The center frequency of the notch filter can be continuously tuned from 13.97 GHz to 41.91 GHz.