We demonstrate the design, analysis, and measurement of an ultra-thin and dual-functional polarization converter to achieve both linear to linear (LTL) and linear to circular (LTC) polarization conversion at the same time. The simulation results illustrate that the LTL polarization conversion can be maintained from 10.1 to 12.3 GHz, 15.0 to 21.0 GHz, and 28.6 to 30.8 GHz with the polarization conversion ratio (PCR) above 80%, and at 11.0, 18.5, and 30.1 GHz, the PCR is nearly 100%. The LTC polarization can be realized in the frequency range of 22.8 to 28.6 GHz, and the axial ratio (AR) is better than 3 dB. In addition, the polarization conversion capability is stable for oblique incident angles up to 15 deg. The experiments are carried out to validate the property, which show that the proposed converter can successfully achieve the broadband LTL and LTC polarization conversion simultaneously with an ultra-thin design. This converter has potential applications in microwave communications, remote sensing, and imaging.