  In a usual dark matter (DM) model without a huge mass difference between the
DM and lighter mediator, using the coupling strength suitable for having the
correct relic density, the resulting self-interaction becomes several orders of
magnitude smaller than that required to interpret the small scale structures.
We present a framework that can offer a solution for this point. We consider a
model that contains the vector DM and a heavier but unstable Higgs-like scalar
in the hidden sector. When the temperature drops below $\sim m_{\rm DM}$, the
hidden sector, which is thermally decoupled from the visible sector, enters a
cannibal phase, during which the DM density is depleted with the
out-of-equilibrium decay of the scalar. The favored parameter region, giving
the correct relic density and the proper size of self-interactions, shows the
scalar-to-DM mass ratio $\in [1.1,1.33]$ and the scalar mass $\in[9,114]\,{\rm
MeV}$. A sizable parameter space still survives the most current constraints
and can be further probed by the near future NA62 beam dump experiment.
