A single and dual-wavelength switchable linear polarization Yb-doped double-clad fiber laser configuration is proposed, in which the resonance cavity is composed of a fiber Bragg grating fabricated in a polarization maintaining fiber and a high reflectivity dichromatic mirror. A cubic polarization beam splitter (PBS) rotating around its own optical axis is inserted between the high reflection cavity mirror and the collimator in the laser cavity, which is used to adjust the polarization to realize single and dual-wavelength lasing emission. The polarization hole burning is enhanced by the selective polarization feedback from the polarization maintaning fiber Bragg grating (PM-FBG). The relationship between polarization states and rotating angle of PBS is analyzed by using Jones matrix, which agrees well with the experimental results. The laser features wavelength of 1070.08 nm and 1070.39 nm, output power of 1.0 W, signal noise ratio of 48 dB, slope efficiency of 34%, as well as a very narrow linewidth of 0.02 nm. The polarization characteristics are studied by measuring the laser power transmitted through a Glan-Thomson polarizer. The polarization state of the laser is linearly polarized with a polarization degree of 13.37 dB when it is lasing at single wavelength, while it is orthogonal polarization laser for dual wavelength operating.