The dielectric constant and the substrate thickness are the important factors which affect the performance of antenna. In order to verify the change in the impedance bandwidth of the microstrip rectangular patch antenna when varying the thickness of the dielectric substrate in the case of the same relative permittivity.In this paper, four rectangular microstrip patch antennas with operating frequency of 1.95 GHz are designed and simulated by using HFSS. The relative permittivity is 2.2, and the thicknesses of dielectric substratesare 0.8, 1.6, 2.4, 3.2 mm.Comparisonhas been made between the four different patch antennas, such as Sparameters chart and pattern. The simulation resultsverify thatat a given frequency, when choosing the same substrate material, the impedance bandwidth is increases when the thickness increasesas described in the related literature.