A tunable, linearly polarized Yb-doped fiber laser, based on a 45°-tilted fiber grating and a fiber Bragg grating with a linear cavity, is proposed. The use of the tilted fiber grating as a linear polarizer provides an output laser with a central wavelength of 1065.90 nm, a 3 dB bandwidth of 0.03 nm, and a polarization extinction ratio higher than 35 dB. The polarization extinction ratio remains stable for 4 h. The temperature characteristics of the beam reflected by the fiber Bragg grating make the central wavelength continuously tunable in the range of 1065.92--1066.87 nm; during the tuning operation, the output polarization extinction ratio is maintained at ≥30 dB.