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For inverse synthetic aperture radar (ISAR) imaging of a maneuvering target, the Doppler frequency shift for the received signal in a range bin is time varying. In this letter, the received signal is modeled as a multicomponent cubic phase signal, and a new ISAR imaging algorithm based on the product generalized cubic phase function (PGCPF) is proposed. The PGCPF algorithm can estimate the parameters of a multicomponent cubic phase signal, and combined with the range-instantaneous-Doppler technique, high-quality instantaneous ISAR images can be obtained. Results of real data demonstrate the effectiveness of the new method presented in this letter.