In this work, we consider the generalized Benjamin-Bona-Mahony equation \(\begin{aligned} \partial _t u+\partial _x u+\partial _x( |u|^pu)-\partial _t \partial _x^{2}u=0, \quad (t,x) \in \mathbb {R} \times \mathbb {R}, \end{aligned}\) with \(p>4\) . This equation has the solitary waves solution \(\phi _{c}(x-ct), \) for any frequency \(c>1.\) It has been proved by Souganidis and Strauss [10] that, there exists a number \(c_{0}(p)>1\) , such that solitary waves \(\phi _{c}(x-ct)\) with \(1<c<c_{0}(p) \) is orbitally unstable, while for \(c>c_{0}(p), \) \(\phi _{c}(x-ct)\) is orbitally stable. The linear exponential instability in the former case was further proved by Pego and Weinstein [9]. In this paper, we prove the orbital instability in the critical case \(c=c_{0}(p)\) .
