We study the dynamics of electroweak phase transition in a simple extension of the Standard Model where the Higgs sector is extended by adding an $SU(2)_L$-mutiplet. By making random scans over the parameters of the model, we show that there are regions consistent with constraints from collider experiments and the requirement for a strong first-order electroweak phase transition which is needed for electroweak baryogenesis. Further, we also study the power spectrum of the gravitational waves which can be generated due to the first-order phase transitions. Observation of such gravitational waves, such as by future space-based gravitational wave detectors, could yield information that is complementary to collider and dark matter experiments.