In terms of the characteristic of solid-state plasma (SSP), which can be switched dynamically between the metallic state and dielectric state through applying an external bias voltage, a reconfigurable bi-functional metamaterial polarization converter based on SSP is designed. Research results show that when SSP is in metallic state, the proposed metamaterial polarization converter can achieve reflective linear-linear polarization conversion within a wider frequency range with polarization conversion efficiency larger than 98%. When SSP is in a dielectric state, the designed converter works in the mode of transmission, and under this circumstance, it can achieve transmissive linear-circular polarization conversion. The background physical mechanism of the polarization conversion is interpreted by the studying the distribution of surface currents under the two states. Furthermore, through changing the structural parameters, changes in polarization conversion performance are studied both for the metallic state SSP and dielectric state SSP, which prove that the proposed SSP-based metamaterial polarization converter not only possesses reconfigurable polarization conversion property, but also can maintain good Robustness to the small change of structural parameters. Both these properties will benefit the experimental verification and real fabrication. Meanwhile, the small change of incident angles will not also bring clear change in the conversion performance, which can ensure real application requirements. As a result, the proposed SSP based reconfigurable metamaterial polarization converter can not only meet the application of different working modes, different conversion characteristics, but also have great potential applications in the area of communication, sensing and detection, imaging, and so on.