A new quaternary superionic conducting AgI-Ag2O-(SeO3 + MoO3) glasses with different compositions of the dopant salt AgI were prepared by rapid melt quenching. The compounds were characterised by X-ray diffraction, scanning electron microscopy and infrared spectroscopy, and glass-forming compounds were identified. The frequency dependence of electrical conductivity, sigma, complex permittivity, epsilon(*), and electrical modulus, M(*), were studied for various compositions of the dopant salt AgI at different temperatures. At room temperature, 293 K, the highest conductivity, sigma=3.12 X 10(-2) S/cm is obtained for the glass with 60% AgI. The ionic conductivity sigma and the complex permittivity epsilon(*) is described in terms of ion diffusion and polarisation. The composition and temperature dependence of the electric modulus M(*) is studied and the results are reported.