We use the semianalytical Cartesian multipole method to investigate the light transmission and reflection spectra of anisotropic dielectric metasurfaces, and extend the multipole decompositions method to account for cross-polarization conversion effects. We observe sharp high-Q resonances arising from a distortion of symmetry-protected bound states in the continuum in asymmetric dielectric metasurfaces, i.e., quasibound states in the continuum. In addition, by further introducing in-plane symmetric breaking perturbation, the polarization conversions of linearly polarized light can be achieved through quasibound states in the continuum. With the aid of temporal coupled-mode theory, we can obtain the limit of cross-conversion under single high-Q resonance, i.e., 0.25. Our work will help to design dielectric metasurfaces to control the polarization states of light.