A simple design of a broadband multifunctional polarization converter using an anisotropic metasurface for X-band application is proposed. The proposed polarization converter consists of a periodic array of the two-corner-cut square patch resonators based on the FR-4 substrate that achieves both cross-polarization and linear-to-circular polarization conversions. The simulated results show that the polarization converter displays the linear cross-polarization conversion in the frequency range from 8 to 12 GHz with the polarization conversion efficiency above 90%. The efficiency is kept higher than 80% with wide incident angle up to 45°. Moreover, the proposed design achieves the linear-to-circular polarization conversion at two frequency bands of 7.42-7.6 GHz and 13-13.56 GHz. A prototype of the proposed polarization converter is fabricated and measured, showing a good agreement between the measured and simulated results. The proposed polarization converter exhibits excellent performances such as simple structure, multifunctional property, and large cost-efficient bandwidth and wide incident angle insensitivity in the linear cross polarization conversion, which can be useful for X-band applications. Furthermore, this structure can be extended to design broadband polarization converters in other frequency bands.