Composites of an expanded graphite/diglycidyl ether of bisphenol A (DGEBA) were prepared by a simple melt blending method, and their dielectric and mechanical properties were investigated. During observations of fractured surfaces of the composites, the graphite sheets were seen to be homogeneously dispersed in the epoxy matrix. Moreover, the composites presented an enhanced dielectric constant ($ 180) and a low loss factor ($ 0.05) at 50 Hz, suggesting their potential suitability for embedded dielectric applications. The enhanced dielectric constant can be explained by the percolation theory and the relatively low loss factor was attributed to strong interfacial interactions between the polymer molecules and the AOH/ACOOH groups of the expanded graphite, which constrained the orientational polarization of the polarons. Furthermore, dynamic mechanical analysis of the composites showed a restricted macromolecular relaxation and improved mechanical properties.