This paper uses Lagrangian differential equations to study the effect of road roughness on the average speed of outdoor trail running. The purpose is to analyze the dynamic model of off-road sports. In this paper, the longitudinal and cross-sectional data of the road are collected and pre-processed, mainly on gravel pavement. Then this paper proposes an approximate formula for the relationship between running speed and road surface roughness. Furthermore, this paper uses the Lagrangian differential equation to solve the road non-uniformity and running speed. Finally, this paper presents an off-road speed prediction method on random uneven road conditions. Finally, the simulation experiments demonstrate that the model based on the Lagrangian differential equation can comprehensively reflect various factors affecting the average outdoor off-road speed. The power spectral density of each sampling point of the model, load input, etc., are all meaningful. This model meets the needs of simulation experiments.