  The spread of a graph $G$ is the difference between the largest and smallest
eigenvalue of the adjacency matrix of $G$. In this paper, we consider the
family of graphs which contain no $K_{s,t}$-minor. We show that for any $t\geq
s \geq 2$, there is an integer $\xi_{t}$ such that the extremal $n$-vertex
$K_{s,t}$-minor-free graph attaining the maximum spread is the graph obtained
by joining a graph $L$ on $(s-1)$ vertices to the disjoint union of $\lfloor
\frac{2n+\xi_{t}}{3t}\rfloor$ copies of $K_t$ and $n-s+1 - t\lfloor
\frac{2n+\xi_t}{3t}\rfloor$ isolated vertices. Furthermore, we give an explicit
formula for $\xi_{t}$ and an explicit description for the graph $L$ for $t \geq
\frac32(s-3) +\frac{4}{s-1}$.
