  For $-1\leq B<A\leq 1$, let $\mathcal{S}^*(A,B)$ denote the class of Janowski
starlike functions which satisfy the subordination relation $zf'(z)/f(z)\prec
(1+Az)/(1+Bz)$. In the present article, we determine the sharp of
pre-Schwarzian norm for the functions in the class $\mathcal{S}^*(A,B)$.
