Storage stability at high temperature is one of the major concerns of styrene–butadiene–styrene (SBS)-modified asphalt. This study aims to address this concern by incorporating nanoclay into SBS-modified asphalt. To achieve this objective, SBS-nanoclay-modified asphalt was prepared with three types of nanoclay and two mixing methods, i.e. directly mixing SBS, nanoclay and base asphalt binder together (direct mixing or DM) and fabricating SBS-nanoclay solid composite first and then mixing the composite with asphalt binder (composite mixing or CM). The rheological properties and storage stability of the SBS-nanoclay-modified binders prepared under different conditions were tested and compared. It was found that all nanoclays increased the viscosity of SBS-modified asphalt, but had insignificant effects on its rutting and fatigue properties, regardless of the mixing method. Among the three types of nanoclay investigated in this study, the one with the lowest hydrophilic property and largest layer gap performed the best, which significantly improved the storage stability of SBS-modified asphalt. Between the two mixing methods, the CM method was more effective than the conventional DM method in terms of storage stability enhancement.