In this paper, the numerical solutions of time fractional Burger’s and coupled Burgers’ equations are obtained using the parametric quintic spline method with a local truncation error of order eight in distance direction. Additionally, the von Neumann method was utilized for studying the stability analysis of the present method. Finally, to show the accuracy of this method, some examples with different cases for Burger’s and coupled Burgers’ equations are presented and their results are compared with the previous methods.