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Installing annular wave-energy converters (WECs) on the columns of floating wind platforms in the form of a coaxial-cylinder provides a convenient means of integration. Extant coaxial-cylinder-type wind-wave hybrid systems are mostly based on single-column platforms such as spars (‘single coaxial-cylinder hybrid system’ hereafter). Systems based on multiple-column platforms such as semi-submersible platforms (‘multiple coaxial-cylinder hybrid systems’ hereafter) are rarely seen or studied, despite their superiority in wave-power absorption due to the use of multiple WECs as well as in dynamic stability. This paper proposes a novel WindFloat-annular-WEC hybrid system, based on our study investigating its dynamic and power features, and optimizing the geometry and power take-off of the WECs. Our results show that the dynamic and power features of a multiple coaxial-cylinder hybrid system are different from those of a single coaxial-cylinder hybrid system, so the same optimization parameters cannot be directly applied. Flatter annular WECs absorb slightly more power in a wider wave-period range, but their geometry is confined by limitations in installation and structural strength. The overall effect of an oblique incident wave is greater intensity in the motions of the hybrid system in yaw and the direction perpendicular to propagation, although the difference is small and may be negligible.