Runge Phenomenon which is a very well-known example and published by C. Runge in 1901 is as follows: polynomial interpolation of a function , using equidistant interpolation points on could diverge on certain parts of this interval even if is analytic anywhere on the interval. Among all the techniques that have been proposed to defeat this phenomenon in the literature of approximation theory, there is the mock-Chebyshev interpolation on a grid: a subset of points from an equispaced grid with points chosen to mimic the non-uniform -point Chebyshev–Lobatto grid . This study suggests a fast algorithm for computing the mock-Chebyshev nodes using the distance between each pair of consecutive points. The complexity of the algorithm is , where is the number of the Chebyshev–Lobatto nodes on the interval . A discussion of bivariate generalization of the mock-Chebyshev nodes to the Padua interpolation points in is given and numerical results are also provided.