  In this paper, we prove that the Cauchy problem for the Fornberg-Whitham
equation is not locally well-posed in $B^s_{p,r}(\R)$ with $(s,p,r)\in
(1,1+\frac1p)\times[2,\infty)\times [1,\infty]$ or $(s,p,r)\in
\{1\}\times[2,\infty)\times [1,2]$ by showing norm inflation phenomena of the
solution for some special initial data.
