A low sidelobe leaky wave antenna (LWA) based on Spoof Surface Plasmon Polariton (SSPP) with switchable right/left-handed circular polarization (CP) and linear polarization (LP) radiation function by controlling the status of two PIN diodes is proposed. Two symmetrical SSPP transmission lines (TLs) are connected through two PIN diodes, and the ON–OFF of diodes constitute three different transmission modes. Two rows of the tapered arranged elliptical patches are loaded periodically around the TL to break the original stable transmission structure for radiation, and suppress the antenna sidelobe levels to less than −10 dB. After experimental verification, the reconfigurable antenna can reach three functionalities: (1) Mode 1: 22°right-handed CP beam scanning from 8.3 to 9.0 GHz; (2) Mode 2: 22°left-handed CP beam scanning from 8.3 to 9.0 GHz; (3) Mode 3: 78°LP beam scanning from 8.3 to 10.3 GHz. In Mode 1 and 2, the axial ratios (ARs) are lower than 3 dB, and the average gain can reach 11.6 dBi, while 13.4 dBi in Mode 3. A leaky wave antenna that can switch the radiation function of linear/circular polarization with favorable performance characteristics, such as wide scanning range, high gain, low sidelobe levels, and high efficiency, makes it an ideal candidate for wireless communication.