<p>A novel short-term time series forecasting scheme based on evolutionary interpolation of Chebyshev polynomials is presented in this paper. The uniqueness of the proposed scheme lies in the higher density of Chebyshev nodes at the ends of the interpolation interval. Thus, the structural representation of the algebraic interpolant closer to the present moment of time becomes more accurate compared to the older Chebyshev nodes. The internal smoothing scheme is used to find a balance between the ability of the algebraic interpolant to reflect the local dynamics and to suppress the unwanted effects outside the interpolation interval. Evolutionary optimization algorithms are used to define near-optimal corrections of nodal values of the time series. The proposed nonlinear mapping scheme used on the last elements of an equally spaced time series enables a more accurate extrapolation of the soft algebraic interpolant. To our knowledge, this is the first attempt to employ non-uniform Chebyshev nodes for the prediction of an equally spaced time series. Computational experiments with several standard time series are used to demonstrate the efficacy and the accuracy of the proposed one-step-ahead forecasting scheme.</p>