Inappropriate speed in negotiating curves is the primary cause of rollovers and sideslips. In this study, the authors proposed an improved curve speed model considering driving styles, as well as vehicle and road factors. On the basis of a vehicle-road interaction model, the driver behaviour factor was introduced to quantify driving styles of curve speed choices. Firstly, the fuzzy synthetic evaluation method was utilised to classify the driving styles of 30 professional drivers into three different types (i.e. cautious, moderate and aggressive). Secondly, the classification results using fuzzy synthetic evaluation were compared to and verified with the K-means clustering method resulting over 60% the similarities. Finally, the proposed curve speed model was built and compared with four existing models. The authors' model has the following promising advantages: (i) it reflects the speed preferences of three different types of drivers on the premise of driving safety on curves; and (ii) it shows a stationary speed transition when the road adhesion coefficient exceeds 0.8, which indicates that rollover, instead of sideslip, becomes the primary cause for lateral instability crashes on curves. Therefore, this proposed curve speed model could be applied in a curve speed warning system to improve both driving safety and comfort.