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In this letter, a new dual-band planar spiral antenna is proposed. This antenna is realized by incorporating a finite frequency-selective surface (FSS) into a planar spiral antenna as its ground plane. Because of the added FSS, a broadband spiral antenna can be transformed into a dual-band antenna. Especially, the main-beam directions associated with these two bands can be widely separated more than 60deg. Therefore, the antenna can be simultaneously applied to satellite and ground-based communications. A prototype of this FSS-added spiral antenna was created and examined. The simulated and measured results obtained demonstrate its promising performance.