The generalized spectral domain-exponential matrix technique (GSD-EMT) is used to investigate the radiation characteristics of a dipole antenna placed on various grounded Faraday chiral substrates, and such Faraday chiral materials include chiroferrite and semiconductor chiroplasma. Numerical results are presented to demonstrate the combined effects of gyrotropy and chirality on the pattern sharp as well as the main beam direction of dipole antenna, and the influences of different constitutive parameters are taken into consideration carefully. It is believed that the present study provide us much insight into the physical properties of Faraday chiral substrates.