Abstract: In this paper, we improve Remes algorithm by simplifying the process of finding maximum points, avoiding solving linear of equations and finding zero points of error function. For an arbitrary continuous function f, we obtain the explicit formula of its nth best Chebyshev approximation on n+2 knots, at the same time, we show the explicit expression of minimal deviation in a very simple way. Finally we obtain the convergence deviation in a very simple way. Finally we obtain the convergence of the improved algorithm and give the analysis of numerical results.