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In this work, a metasurface with the symmetrical double C-shaped narrow ring connected with the central cross structure is investigated by simulation, theory and experiment, which can near-perfectly convert linearly polarized electromagnetic waves into their orthogonal components in the frequency ranges from 9.38 to 13.36 GHz and 14.84 to 20.36 GHz. And the corresponding fractional bandwidths within the two bands are 35.00% and 31.36%, respectively. The influences of structural parameters on the polarization conversion performance are studied. The results show that the central frequencies and bandwidths of the two bands can be easily modulated by varying the structural parameters of r and θ. The high-efficiency and dual-broadband characteristics can also be well maintained in the oblique incidence range of 0-45°. Meanwhile, the mechanisms of polarization conversion are analysed, and several formulas are used to calculate the reflection coefficients of the co-and cross-polarization under the normal incident y-polarized electromagnetic waves based on the phase difference of the reflection coefficients of the uand v-polarized conversions. The experiment results are in good agreement with those of simulations and theoretical analysis. The proposed metasurface has important applications in novel polarization control devices.