We demonstrated an all-fiber comb filter that can continuously tune the wavelength for four switchable wavelength spacings. The comb filter consists of a fiber loop mirror (FLM) that is inserted with three polarization maintaining fibers (PMFs) and three polarization controllers (PCs). The transmission characteristics of the comb filter was theoretically analyzed. The output characteristics of the comb filters shows a dependence of the orientation angles of the PCs. With the angles being optimally set, the comb filter with four different wavelength spacings can be achieved. The wavelength continuously tunable and wavelength spacing variable mechanisms are elaborated. The three PCs are employed to enable the tunable and switchable functions. The two PCs between the PMFs serve as a polarization rotator to align the birefringent axes of the PMFs for varying the wavelength spacing while the PC adjacent to the optical coupler can be used for wavelength tuning function. When the two quarter-waveplates (QWPs) of the PC are optimally set at π/4 and - π/4, the half-waveplate (HWP) acts as a wavelength tuning element, and when the QWPs are set at zero degrees, the HWP serves as an amplitude tuning element. The center wavelength of the comb filter could be linearly tuned with the rotation angle of the HWP, and a π/2 change in the rotation angle leads to a wavelength change in one free-spectral-range (FSR). A π/4 change in the rotation angle could bring the normalized peak transmission from its maximum at 1 to minimum at 0. The proposed tunable technique has been verified by our experimental results. We experimentally demonstrated the comb filters can switch among FSRs of 0.75 nm, 1.01 nm, 1.51 nm, and 3.1 nm with tunable functions.