A styrene-butadiene-styrene (SBS) latex modifier can be used for asphalt modification due to the fact of its energy-saving, construction convenience, and economic advantages. The objective of this study was to investigate the influence of asphalt type and SBS latex dosage on the rheological properties, compatibility, and storage stability of asphalt through temperature and frequency sweep, steady-state flow, multiple stress creep and recovery (MSCR) tests, Cole-Cole plots and thermal storage tests. The results indicated that high SBS latex content is beneficial for improving anti-rutting, anti-fatigue, viscous flow resistance, and elastic recovery abilities of modified asphalt. The chemical composition of asphalt had a significant effect on the properties of the SBS latex-modified asphalt. High asphaltenes and low resins were favorable to enhancing anti-rutting and recovery properties but weakened the anti-fatigue, compatibility, and storage stability of modified asphalt. Furthermore, compared to SBS particle-modified asphalt, SBS latex-modified asphalt had greater rutting and fatigue resistance. However, SBS latex-modified asphalt had some disadvantages in compatibility and storage stability. Comprehensively considering the balance of viscoelastic properties, compatibility, and storage stability of SBS latex-modified asphalt, the mixing dosage of SBS latex modifier is recommended at 4.0 wt% which could feasibly replace SBS particle in asphalt modification.