This paper presents a numerical scheme based on the Galerkin finite element method and cubic B-spline base function with quadratic weight function to approximate the numerical solution of the time-fractional Burger's equation, where the fractional derivative is considered in the Caputo sense. The proposed method is applied to two examples by using the $L_2$ and $L_{\mathrm{\infty }}$ error norms. The obtained results are compared with a previous existing method to test the accuracy of the proposed method.