The finite-difference method applied to the time-fractional subdiffusion equation usually leads to a large-scale linear system with a block lower triangular Toeplitz coefficient matrix. The approximate inversion method is employed to solve this system. A sufficient condition is proved to guarantee the high accuracy of the approximate inversion method for solving the block lower triangular Toeplitz systems, which are easy to verify in practice and have a wide range of applications. The applications of this sufficient condition to several existing finite-difference schemes are investigated. Numerical experiments are presented to verify the validity of theoretical results.