The authors propose a Crank-Nicolson-type difference scheme for solving the subdiffusion equation with fractional derivative. Only a tridiational linear system needs to be solved at each temporal level. The solvability, unconditional stability, and
norm convergence are proved. The convergence order is
in the temporal direction and two in the spatial direction. Using the Sobolev embedding inequality, the maximum norm error estimate is obtained. A spatial compact scheme based on the Crank-Nicolson-type difference scheme with the convergence order of
is also presented. Numerical examples support the theoretical analysis. Comparisons with the related existing works are presented to show the effectiveness of the present method. This is an interesting paper.