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This article demonstrates a planar dual-band array antenna for millimeter-wave applications, which has a left-hand circular polarization and a right-hand circular polarization for two operating bands, respectively. By using aperture-fed stacked-curls, the proposed antenna can attain broad axial ratio (AR) bandwidths in both K- and Ka-bands through a single port. Meanwhile, two stacked-curls are designed to rotate in different directions for achieving orthogonal circular polarizations in two bands, respectively. An <inline-formula> <tex-math notation="LaTeX">$8\times 8$ </tex-math></inline-formula> stacked-curls array antenna is designed and manufactured for verifications. The measured 3 dB AR bandwidths are 11.59&#x0025; (18.7-21 GHz) in the K-band and 9.93&#x0025; (26.8-29.6 GHz) in the Ka-band, with reflection coefficient lower than &#x2212;10 dB. The maximum gain in K- and Ka-bands are 18.59 dB and 18.13 dB, respectively. The proposed antenna can be used for developing compact satellite communication systems.