Abstract: In order to study the traffic flow speed-density relationship under the condition of heterogeneity, the fundamental diagram model of speed-density relationship of stochastic traffic flow is established based on random-parameter linear regression. The random-parameter linear regression is used to fit the relationship between speed and density, and the random parameters are tested and the error of the model is analyzed. The calculation results show that the Greenshields, Greenberg, Underwood and Northwestern model with random parameter reflect the influence of traffic flow heterogeneity on the relationship between speed and density, and the average absolute errors of the four random parameter models is reduced by 57.04%, 81.30%, 74.48%, and 52.27% respectively, compared with the corresponding fixed parameter model. The proposed method can be extend to different fundamental diagram of traffic flow speed-density relationship, reflecting the characteristics of different datasets, and has an important application in traffic flow theory.