The $Co^{60}$ $gamma$-ray irradiation effects on the electrical and thermal characteristics of low density polyethylene crosslinked by Dicumyl peroxide (DCP) were investigated. We experimented on electrical properties as following; electrical tree inception and growing type for applying AC step voltage, AC breakdown strength, volume resistivity with increasing dosage. Also, chemical analyses were performed TGA, gel fraction. These electrical properties changed depending upon its crosslinking degree and byproducts from crosslinking reactions. Crosslinking reactions were considered causing by $gamma$-ray irradiation and DCP had contained in low density polyethylene.