Abstarct: Quarkoniums are heavy mesons like which have important effects on the study of hadronic and plasma phases of QCD. In this thesis, using string theory we study the potential of this class of mesons. By considering a meson as a quark-antiquark pair, we use the AdS/CFT correspondence and it is shown that by considering the gravitational corrections the dissociation length of heavy meson decreases. The background geometry is RN AdS black holes. Our study confirms that for melting of heavy mesons, one needs higher temperatures. To study excited states of the meson, we consider rotating mesons. It is shown that as the spin increases, the dissociation length also increases. The results of our study can be compare with the experiments in the RHIC and LHC. In addition, we find that the mechanism of meson melting in hadronic phase and plasma phase are the same. Then the abstract of must be corrected which was confirmed by the correspondence Author.