  Under the framework of the vector meson dominance model (VMD), the absolute
scattering lengths of light vector mesons ($\phi$, $\omega$, and $\rho$) with
the deuteron are calculated from the cross sections of vector meson
photoproduction off a deuteron. Additionally, a fitting function is used to
predict the scattering lengths of the heavy vector mesons $J/\psi$-$d$ and $%
\Upsilon$-$d$. Based on these results, the distribution of the scattering
lengths $|\alpha_{V d}|$ between vector mesons and the deuteron is presented
for the first time and compared with the scattering lengths $|\alpha_{V p}|$
between vector mesons and the proton. It is found that as the mass of the
vector meson increases, the scattering lengths $|\alpha_{V d}|$ become closer
to $|\alpha_{V p}|$. In addition, the correlation analysis indicates a strong
positive relationship between the scattering length and the vector meson
radius, with a high correlation coefficient. The implications of results are
essential for improving our understanding of the interaction between hadron and
nucleus.
