Natural rubber latex (NRL) is a polymer material collected from rubber trees with polyisoprene as the main component, which is a sustainable renewable material. With many excellent physical properties, it has been used to modify petroleum asphalt for paving roads very early to improve the performance of asphalt and asphalt mixtures. In order to prepare a modified asphalt with good comprehensive performance, this paper mixes NRL and styrene-butadiene-styrene (SBS) latex to prepare a composite-modified asphalt and conducts the experimental test of the penetration grading system and the experimental test of the rheological index. To obtain a modified asphalt with good comprehensive performance, NRL and SBS latex are mixed in this study to prepare a composite-modified asphalt, and the penetration grading system and rheological index are tested experimentally. The experimental results show that the addition of NRL and SBS latex significantly improves the anti-aging performance of asphalt. Fluorescence microscopy observations show that when the ratio of NRL latex to SBS latex is 1:1 to 1:2, the microstructure of the modified asphalt appears as a bicontinuous phase that interpenetrates the asphalt and latex phases and forms a stable grid. The rutting experiment and low-temperature trabecular bending experiments show that both the high- and low-temperature performance of the NRL/SBS latex composite–modified asphalt mixture improve greatly compared with that of NRL latex–modified asphalt mixture. Furthermore, the water immersion Marshall test and freeze–thaw splitting test show that the NRL-modified asphalt mixture has good resistance to water damage.