Abstarct: Already the potential of the quark-antiquark in string theory has been studied.In this thesis,we study the imaginary part of the potential by consideringthermal fluctuations around the bottom of the classical string.Such an imaginary part arises also in perturbative Quantum Chromodynamics (pQCD). Therefore, energy levels in this potential are not sharp because they acquire a thermal width. In this thesis, our goal is study of thermal width of Quarkoniums with using the AdS/CFT correspondence. Already in theory Supersymmetric Yang-Mills (SYM) thermal width has been calculated and the results obtained in the paper [8]. Repeating the calculations, we show that the results should be changed after correcting errors of the integration path. For comparison with the experimental solutions, the gravitational corrections have been considered. The curvature squared corrections are relevant to the geometry of the Gauss–Bonnet with a coupling constant . In resumption, Upsilon Quarkonium thermal width spectrum for various values of are computed and one finds that the thermal width becomes maximum in a special value of and in this point thermal width becomes larger. Other correction is correction which denoted by . Repeating the calculations of the thermal width spectrum for various values of (t’Hooft coupling), shows that these corrections decreases the values of thermal width. Other correction that we consider in this thesis is adding quark matter to the medium of the plasma. So, the charged black hole should be considered and for explanation of quark matter we must introduce a gauge field that satisfies Maxwell and Einstein equations. In the next, we calculate thermal width in the presence of chemical potential quantity and find that thermal width spectrum with respect to chemical potential has a maximum that this maximum is function of the temperature.