•The effect of adding Naphthenic oil into SBS modified asphalt was compared with adding Nano-MMT.•An ‘ingredients microstructure’ model was proposed for SBS modified asphalt.•The influence of naphthenic on SBS modified asphalt was divided into three stages while only one for Nano-MMT.•Naphthenic oil takes effect as a supplement for maltene. Naphthenic oil is an organic solvent whose effect as an additive to SBS modified asphalt is rarely studied. The influence of naphthenic oil on SBS modified asphalt was investigated in the paper. The influence of a well-known inorganic solid additive, Nano-MMT, was also studied to make a comparison. Storage stability, low/high temperature properties, and rheology were tested with different additive dosages. It is found that the storage stability of SBS modified asphalt can be improved by both Nano-MMT and naphthenic oil. Low temperature property is improved by naphthenic oil but worsened by Nano-MMT. High temperature viscosity is enhanced by naphthenic oil and decreased by Nano-MMT. High temperature sensitivity reflected by softening point and rutting factor increases with Nano-MMT, while it rises first then falls with naphthenic oil. An ‘ingredients microstructure’ model was proposed to describe the microstructure of ingredients of SBS modified asphalt. The model considers SBS modified asphalt to consist of two domains; one is the bee structures domain which contains maltenes inside, the other one is maltene domain which also contains asphaltenes. SBS which is smaller than the bee-like structure is randomly distributed in the maltene. Under the proposed model, the mechanism of naphthenic oil is divided into three stages considering the variation of dosage of naphthenic oil, while the effect of Nano-MMT has only one stage. It was found that the model proposed can explain the changes in storage stability and properties of SBS modified asphalt. It is proved practical to consider naphthenic oil as a supplement for maltene, taking effect in the mixture as saturates and aromatics.