  We provide an upper bound for the Gromov width of compact homogeneous Hodge
manifolds $(M, \omega)$ with $b_2(M)=1$. As an application we obtain an upper
bound on the Seshadri constant $\epsilon (L)$ where $L$ is the ample line
bundle on $M$ such that $c_1(L)=[\frac{\omega}{\pi}]$.
