Abstract: Predictive type of Chebyshev polynomials are an extension of the Chebyshev polynomials and the best approximation theory, it can solve the general forecast predicted the knowability and controllability problems. Through discussions in the article pointed out, when the prediction error of not more than the known maximum absolute error, predicts will become known; when the prediction interval of not more than the known maximum range, the prediction will be controlled. Based on this principle, the prediction function predictive Chebyshev polynomials, Gn(x) polynomials are established. The polynomials based on differential equations, definitions, properties, mathematical tables, the existence of polynomial problems are demonstrated. The predictive type of the best approximation of g(x) polynomials, at y(x)≠0 conditions by Gn(x) polynomials posed, are provided. A specific algorithm to achieve the g(x) polynomials is presented. A way to make predictions closer to the actual value of the error compensation method is introduced, and some examples are given.