We investigate the guiding modes of spoof surface plasmon polaritons (SPPs) on a symmetric ultra-thin plasmonic structure. From the analysis, we deduce the operating frequency region of the single-mode propagation. Based on this property, a spoof SPPs lowpass filter is then constituted in the microwave frequency. By introducing a transmission zero at the lower frequency band using a pair of stepped-impedance stubs, a wide passband filter is further realized. The proposed filter is fed by a transducer composed of a microstrip line with a flaring ground. The simulated results show that the presented filter has an extremely wide upper stopband in addition to excellent passband filtering characteristics such as low loss, wide band, and high square ratio. A prototype passband filter is also fabricated to validate the predicted performances. The proposed spoof-SPPs filter is believed to be very promising for other surface waveguide components in microwave and terahertz bands.