The spectral collocation method has gained great interest for many researchers in the last decade due to the rapid development in obtaining the optimal solution for real phenomena in the environment around us. In this paper, we used fully different spectral collocation method (SCM) than any SCM used in other papers to solve the one- and two-dimensional Burger’s equations. Chebyshev and the shifted Chebyshev polynomials of the first kind are constructed in all directions. The time and the spaces steps are equally discretized for each axis. Numerical results and numerical comparisons with several recently numerical techniques indicate that the suggested scheme is more accurate than the other techniques.