Ground-Penetrating Radar (GPR) has been widely used for non-destructive testing of earth dam disease. However, the forward simulation of GPR for earth dam disease often employs layered homogeneous models, neglecting the influence of medium randomness on its wave field characteristics. Therefore, considering the randomness of the medium, a geoelectrical model for earth dam disease is established, which is based on the mixed-type autocorrelation function and the finite element time-domain method. The influence of random medium model parameters on the single-channel wave of GPR is analyzed. The electromagnetic wave propagation characteristics under different medium models are explored. The forward simulation of GPR for earth dam disease such as panel voiding, concentrated seepage, and loosening are performed. The differences in propagation characteristics for earth dam disease between uniform medium model and random medium model are compared. Compared to the calculation results of the uniform medium model, the propagation speed and amplitude of electromagnetic waves in the random medium model changes, and a number of diffraction waves are present. When performing forward simulation of GPR for earth dam disease, considering medium randomness can deepen the understanding of the GPR section view and help improve the accuracy of image interpretation.