A novel implicit high-order compact difference scheme is established for the time-fractional Burgers’ equation based on a newly developed nonlinear compact operator and the reduction order technique under the uniform mesh and graded mesh. Uniqueness, boundedness, convergence in the pointwise sense and stability in L-norm of the discrete solutions are proved by the Browder fixed point theorem and energy argument. Numerical examples with the smooth solution and nonsmooth solution are provided to confirm numerical theoretical results and demonstrate the efficiency of the high-order compact difference scheme.