Tomlinson-Harashima precoding (THP) is considered as a prominent precoding scheme due to its capability to cancel out the known interference at the transmitter side. Therefore, the information rates achieved by THP are superior to those achieved by conventional linear precoding schemes. In this paper, a new lower bound on the achievable information rate by the regularized THP under additive white Gaussian noise (AWGN) channel with multiuser interference is derived. Analytical results show that the lower bound derived in this paper is tighter than the original lower bound particularly at low SNR range, while both lower bounds converge to the same lower limit as SNR$ ightarrow$$infty$.