Abstract: Two finite difference methods for time-fractional subdiffusion equation with Dirichlet boundary conditions are developed.The methods are unconditionally stable and convergent of order(τ^q+h²) in the sense of discrete L² norm,where q(q=2-β or 2) is related to smoothness of analytical solution to subdiffusion equation,β(0 < β < 1) is order of the fractional derivative,τ and h are step sizes in time and space directions,respectively.Numerical examples are provided to verify theoretical analysis.Comparisons with other methods are made,which show better performances over many existing ones.