We consider gravitational waves in an electroweakly interacting vector dark matter (DM) model. The gauge symmetry of the model is ${\rm SU}(3)_C\times{\rm SU}(2)_0\times{\rm SU}(2)_1\times{\rm SU}(2)_2\times {\rm U}(1)_Y$, and an exchange symmetry between ${\rm SU}(2)_0$ and ${\rm SU}(2)_2$ is imposed to ensure the stability of the DM. Above the electroweak scale, phase transition ${\rm SU}(2)_0\times{\rm SU}(2)_1\times{\rm SU}(2)_2 \to {\rm SU}(2)_L$ occurs. All new particles in the model are bosons, and the new gauge couplings can be relatively large within the perturbative regime. Thus, a potential barrier is easily produced during the phase transition. Consequently, the phase transition can be strongly first-order and produces detectable gravitational waves. The results depend on $m_{h'}$, which is the mass of the $Z_2$-even new scalar particle under the exchange symmetry, and on $m_V$, which is the mass of the vector DM. We find that the model can be tested by future observations of the gravitational waves from the first-order phase transition if 2.5 TeV $\lesssim m_{h'} \lesssim$ 3.5 TeV for $m_V =$ 7 TeV, 1.6 TeV $\lesssim m_{h'} \lesssim$ 2.5 TeV for $m_V =$ 5 TeV, and 2.8 TeV $\lesssim m_{h'} \lesssim$ 3.5 TeV for $m_V = 3$ TeV, respectively.
Comment: 30 pages, 8 figures, 1 table