We consider a novel scenario for Vector Strongly Interacting Massive Particle (VSIMP) dark matter with local SU(2)X ×U(1)Z′ symmetry in the dark sector. Similarly to the Standard Model (SM), 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 the U(1)Z′-charged gauge boson of SU(2)X (X±) becomes a natural candidate for SIMP dark matter, annihilating through 3 → 2 or forbidden 2 → 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 SM hypercharge. 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.