A finite difference scheme which depends on a new approximation based on an extended cubic B-spline for the second order derivative is used to calculate the numerical outcomes of time fractional Burgers equation. The presented scheme uses Caputo’s formulation for the time derivative. Finite difference method will be used to discretize the Caputo’s fractional derivative. The proposed scheme will be shown to be unconditionally stable by Von-Neumann method. The convergence analysis of the numerical scheme will be presented of order O (h 2+ τ 2-α). The presented scheme is tested on four numerical examples. The numerical results are compared favorably with other computational schemes.