We present experimentally a double-arrow metasurface for high-efficiently manipulating the polarization states of electromagnetic waves in the dual-band. The metasurface is capable of converting a linearly polarized (LP) incident wave into a circularly polarized (CP) wave or its cross-polarized LP wave at different frequencies. It is numerically shown that in the two bands from 14.08 to 15.71 GHz and from 17.63 to 19.55 GHz the metasurface can convert the LP wave into CP wave, of which the axis ratio is lower than 3 dB. Meanwhile, the proposed metasurface also can convert the LP wave into its cross-polarized LP wave at 13.39 GHz and 20.29 GHz. To validate the theoretical analysis and simulated results, a prototype is fabricated and measured. The experimental results are reasonably consistent with the theoretical and simulated results, which demonstrates that such a metasurface can successfully achieve dual-band and dual-mode polarization conversion.