  We study the issue of black hole entropy in the topologically massive
gravity. Assuming that the presence of gravitational Chern-Simons term with the
coupling $1/\mu$ does modify the horizon radius $\tilde{r}_+$, we propose
$\tilde{S}_{BH}=\pi \tilde{r}_+/2G_3$ as the Bekenstein-Hawking entropy. This
entropy of CS-BTZ black hole satisfies the first-law of thermodynamics and the
area-law but it is slightly different from the shifted-entropy $S_c=\pi
r_+/2G_3+ (1/\mu l)\pi r_-/2G_3$ based on the BTZ black hole with outer $r_+$
and inner horizon $r_-$. In the case of $r_-=0$, $\tilde{S}_{BH}$ represents
the entropy of non-rotating BTZ black hole with the Chern-Simons term
(NBTZ-CS), while $S_c$ reduces to the entropy of NBTZ black hole. It shows that
$\tilde{S}_{BH}$ may be a candidate for the entropy of the CS-BTZ black hole.
