  In this article, we study the $L^{2}$-harmonic forms on the complete
$2n$-dimensional symplectic hyperbolic manifold. We extend a vanishing of
K\"{a}hler hyperbolic manifold proved by Gromov to symplectic case. Precisely,
we prove that the spaces of $L^{2}$-harmonic forms of bi-degree $(p,q)$ vanish
unless $p+q=n$.
