To simultaneously improve the impact strength and dielectric properties of cured epoxy (EP), herein we explore liquid rubber toughened EP based on a nonpolar epoxidized hydroxyl-terminated polybutadiene (EHTPB), where the rubber is covalently bonded to the EP. Fourier transform infrared and nuclear magnetic resonance proved the chemical reaction between EHTPB and EP, which makes the immiscible EHTPB-EP blend change to compatible one. The results indicate that both the impact strength and dielectric properties can be visibly enhanced with the addition of EHTPB and the maximum values are obtained at 10 phr of EHTPB loading. The improved mechanical toughness can be ascribed to the extensive shear yielding induced by the uniformly dispersed EHTPB domains and the enhanced interfacial compatibility between the two components. Moreover, the enhanced electrical resistivity and dielectric breakdown strength as well as the reduced dielectric constant and loss for the EHTPB-EP can be attributed to the combination of the excellent insulating properties of HTPB and dielectrically favorable interfaces. Therefore, the EHTPB-EP with a concurrent improvement in impact strength and dielectric properties can be used as promising insulating materials for high-frequency microelectronics and high-voltage electrical equipment.