  We consider a novel scenario for Vector Strongly Interacting Massive Particle
(VSIMP) dark matter with local $SU(2)_X\times U(1)_{Z'}$ symmetry in the dark
sector. Similarly to the Standard Model, after the dark symmetry is broken
spontaneously by the VEVs of dark Higgs fields, the approximate custodial
symmetry determines comparable but split masses for $SU(2)_X$ gauge bosons. In
this model, we show that $U(1)_{Z'}$-charged gauge boson of $SU(2)_X$ ($X_\pm$)
becomes a natural candidate for SIMP dark matter, annihilating through
$3\rightarrow 2$ or forbidden $2\rightarrow 2$ annihilations due to gauge
self-interactions. On the other hand, the $U(1)_{Z'}$-neutral gauge boson of
$SU(2)_X$ achieves the kinetic equilibrium of dark matter through a gauge
kinetic mixing between $U(1)_{Z'}$ and Standard Model. We present the parameter
space for the correct relic density in our model and discuss in detail the
current constraints and projections from colliders and direct detection
experiments.
