A single-and dual-wavelength switchable polarized Yb-doped double-clad fiber laser around 1120 nm based on a pair of fiber Bragg gratings (FBGs) is demonstrated. The polarization-maintaining (PM) linear cavity is composed of a double clad PM Yb-doped fiber (YDF) and a pair of PM FBGs. The laser can operate in stable dual-wavelength or wavelength-switching modes due to the polarization hole burning (PHB) and the spatial hole burning (SHB) enhanced by the PM linear cavity. In dual-wavelength operation, the two orthogonally polarized wavelengths are centered at 1118.912 nm and 1119.152 nm, with an interval of 0.24 nm and a signal to noise ratio (SNR) of 35 dB. The maximum output power is 14.67 W when the launched LD pump is 24 W corresponding to an optical efficiency of 61.1%. The lasing lines switchover may be realized by adjusting the polarization controller (PC) fitted in the cavity. The two single-wavelengths are 1118.912 nm and 1119.152 nm. When the injected LD pump is 24 W, the highest output powers are 7.68 W and 8.64 W corresponding to optical efficiencies of 32% and 36% respectively. The spectral linewidth of the lasing lines are 0.075 nm and 0.07 nm, and the average numerical values of PER are 20.3 dB and 19.9 dB, respectively.