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The Chirp-Fourier transform is one of the most important tools of the modern signal processing. It has been widely used in the fields of ultrasound imaging, parameter estimation, and so on. The key to its application lies in the sampling and fast algorithms. In practical applications, nonuniform sampling can be caused by sampling equipment and other reasons. For the nonuniform sampling, we utilized function approximation and interpolation theory to construct different approximation forms of Chirp-Fourier transform kernel function, and proposed three fast nonuniform Chirp-Fourier transform algorithms. By analyzing the approximation error and the computational complexity of these algorithms, the effectiveness of the proposed algorithms was proved.