Waste plastic pollution is a serious issue. In order to adhere to the concept of green development and rationally dispose of polyethylene waste plastic products, polyethylene (PE)-modified asphalt was prepared using recycled polyethylene (RPE) and low-density polyethylene (LDPE) as raw materials. The chemical structures of the RPE- and LDPE-modified asphalt were studied using a Fourier transform infrared spectrometer (FTIR), and the dispersion of RPE was studied using a fluorescence microscope (FM). Subsequently, the modification mechanism of the PE-modified asphalt was revealed. The physical properties and high- and low-temperature rheological characteristics of the PE-modified asphalt were examined using physical property tests, a dynamic shear rheometer (DSR), and a bending beam rheometer (BBR). The creep performance of the PE-modified asphalt was analyzed using multiple-stress creep recovery (MSCR). In addition, a laboratory-made inexpensive inorganic stabilizer was added to enhance the storability of the PE-modified asphalt. The results show that PE and asphalt are similarly compatible and form an S-C bond with an inorganic stabilizer. The resulting product’s storage stability is enhanced via the cross linking between the PE and asphalt and the subsequent formation of a network structure. The segregation softening point increased from 2 °C to 45 °C with the increase in PE content, and the increase in RPE was more obvious than that of LDPE. The high-temperature failure of the 2–6% RPE-modified asphalt can reach 70 °C, while that of the 8% RPE-modified asphalt can reach 76 °C. Low-temperature performance was reduced slightly: the 8% PE-doping low-temperature failure temperature was −14.7 °C. The low-temperature performance was somewhat reduced, but it was still within a PG rating.