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This paper presents an accelerating Nonuniform Fast Fourier Transform (NUFFT) algorithm for imaging reconstruction of two-dimensional synthetic aperture radiometer. This algorithm relies on a mixture of the fast Gaussian gridding algorithm and the judicious use of the FFT on an oversampled grid. It is not limited for an equal spaced visibility function sampling, and has the advantage in storage compared with the traditional gridding method. It is also beneficial for the system optimization by testing a new antenna array configuration. The numerical simulation results indicate that the proposed algorithm is accurate and high-speed.