A single-layer reflective metasurface with linear-to-linear polarization and circularly polarized reflection under linearly polarized incident wave is investigated in this work. The unit cell of our designed metasurface is formed by the inner cross structures and the outer two pairs of serpentine lines etched on the substrate, and metallic copper is attached to the back of the substrate. The simulation results are as follows that the linearly polarized reflected wave in the middle frequency ranges of 9.33–11.77 GHz (the fractional bandwidth of 23.1% and the polarization conversion ratio over 95%) is realized when the co-polarization reflection coefficients are within −14 dB under the y-polarized illuminated wave. Besides, the linear-to-circular polarization state is completed when the y-polarized wave impinges on this metasurface in two nonadjacent frequency bands from 5.95 to 8.80 GHz and 12.68 to 15.58 GHz, which are corresponding to the relative bandwidth of 38.6% and 20.5% respectively according to the 3 dB axial ratio bandwidth property. In addition, the physical mechanism is explained and the sample of this metasurface converter is manufactured and tested. The experiment results are corresponding to the simulation results, which prove the reliability of the simulation results.