In this paper, a triple-band reflective polarization converter with high efficiency for both linear-to-linear and linear-to-circular polarizations based on a metasurface is proposed, which can rotate a linearly polarized (LP) incident wave into its orthogonal direction with over 90% polarization conversion ratio (PCR) in the bands of 5.5-5.9 GHz (relative bandwidth of 7%) and 12-17.7 GHz (relative bandwidth of 38.4%). Besides, the proposed converter can also transform a linearly polarized incident wave to circularly polarized (CP) wave in the band of 6-12 GHz (relative bandwidth of 66.7%). Additionally, the performance of proposed polarization converter stays in considerable stability with the incident angle increasing 60˚ in circular polarization and 30˚ in linear polarization. Moreover, the physical mechanism of multiple resonances is discussed based on surface current distributions and equivalent circuit model. A prototype of the proposed converter is fabricated and measured, and the experiments and simulations are in great agreement. This polarization converter can be employed to manipulate the polarization of the signal in microwave communication.