Based on the practical and importance of the Chebyshev interpolation polynomial algorithm, in order to structure Chebyshev interpolation polynomial of high precision possible, having some research on the Chebyshev interpolation polynomial algorithm firstly: giving the conditions under the usage of the Chebyshev interpolation polynomial and Lagrange interpolation polynomial, utilizing numerical simulation experiment to change the equidistant interpolation by the Lagrange interpolation polynomial interpolation algorithm into the transformation of the not equidistant interpolation by the Chebyshev interpolation polynomial interpolation algorithm image directly. Secondary, the algorithm error analysis is discussed between the Lagrange interpolation polynomial interpolation and the Chebyshev interpolation polynomial interpolation. Finally, under the case of the number of nodes is equal to or greater than five that the conditions on which the usage of Chebyshev interpolation polynomial and Lagrange interpolation polynomial are given.