A dual-band angular-stable transmissive linear to circular polarization converter based on metasurface is proposed and demonstrated in this work. The converter consists of three layers. The top and bottom layers are formed by an array of double split-ring layers. The unit cell of the central layer contains a square loop nesting a slant dipole. The split-rings create two resonances, enabling dual-band operation. The slant dipole and square loop are useful for improving the quality of circular polarization conversion. It is shown that the proposed polarization converter converts the incident linearly polarized wave into circularly polarized wave with opposite polarization modes over the frequency ranges of 8.77–10.58 and 17.59–19.88 GHz. The angular stability is up to 60° for 3 dB axial ratio. Moreover, the thickness of unit cell has a wavelength below 0.06 at the lower band. Compared with other designs in the literature, the structure bears merits of wideband response, high angular stability, and low-profile property within dual-band operational region. To validate the design, a sample prototype was designed, fabricated, and measured. The measured results are in good agreement with the simulated ones.