The graphene oxide/off-stoichiometric thiol-ene (GO/OSTE) composites was prepared via a “click” chemical reaction. Experimental results from SEM, Raman, and XPS analyses demonstrated that GO can be well-incorporated into the OSTE matrix, with covalent crosslinking occurring between the surface functional groups of GO and the OSTE polymer. Thermogravimetric analysis (TGA) results indicated that the GO/OSTE composites exhibit excellent thermal stability below 350 °C. It was found that the dielectric constant, dielectric loss, and electrical conductivity of the GO/OSTE composites is strongly dependent on the GO content and frequency. The dielectric constant of the GO/OSTE composites increases with the increase of GO content, attributed to enhanced interface polarization effects and dipole polarization responses. When the mass fractions of GO is about 0.06 wt%, the measured dielectric constant of the composite material at 103 Hz is about 23.6, approximately six times than that of the OSTE matrix. At 107 Hz, the electrical conductivity also increases by about ten-fold, likely attributed to the hopping motion of charge carriers under high-frequency electric fields.