Abstarct: In this thesis, we study the holography of gravitational waves from the first-order cosmic phase transition of quantum color dynamics (QCD). When the Universe was about 10-10 seconds old, the electro-weak phase transition occurs by breaking the symmetry between the weak and electromagnetic interactions. About 10-5 after the big bang, the phase transition from the quark–gluon plasma to the hadronic phase happened. Since, in the early universe first-order phase transitions can also generate gravitational waves, in this thesis, we study the cosmological first-order QCD phase transition and we calculate the gravitational waves spectrum of the bubble evolution with holographic models. Using AdS/QCD and the correspondence between a first order Hawking-Page phase transition and de/confinement phase transition, we obtain the resulting gravitational wave spectrum in the presence of the Gauss-Bont coupling. We also show that μ-Ares, Tiaji and SKA detectors will be able to detect these gravitational waves, which can be an evidence for the first order deconfinement transition. On the other hand, gravitational waves are dependent on coupling, We consider these waves to have a limited bariochemical potential and obtain key quantities characterizing the gravitational wave energy density spectrum. We conclude that sound waves play an important role in the spectrum. We also consider a supercooling scenario during the QCD phase transition and show that the gravitational waves generated during this period can be detected by FAST, NANOGrav, μ-Ares, Tiaji, IPTA and SKA experiments. In the following, we focus on the approach of dilaton/radion dominance approximation. We find the dual bounce action and the duration of the phase transition at the nucleation temperature and obtain the quantities characterizing the gravitational wave spectrum through this approach for prompt phase transition and supercooled regime.