In this paper, a new chirp scaling(CS) algorithm based on Chebyshev polynomials is proposed. The new algorithm uses Chebyshev polynomials interpolation instead of the Taylor series expansion to gain a new expression of the 2D spectrum, based on which the complete imaging process is developed. This paper analyzes the residual error of the new algorithm and the traditional one, compares the value and spatial variance and discusses the difference in imaging quality and range segmentation. Theoretical analysis shows that the new algorithm possesses high accuracy and less spatial variant error which results in the improvement of imaging and reduction of range segmentation. In the end, computer simulations confirm the validity of the algorithm.