Surfactants can reduce the surface tension of fluid interfaces and significantly alter the wetting properties of solid surfaces, making them widely used in industrial production. In order to investigate the motion characteristics of surfactant-laden droplets on solid surfaces, a mixed model incorporating soluble surfactant flow and contact line dynamics was established based on the Cahn-Hilliard phase field lattice Boltzmann method, and the Yokoi dynamic contact angle model considering the speed of three-phase contact line movement obtained from experiments. A computational program was independently developed based on the governing equations, and parallel processing was used to improve computational efficiency. Subsequently, the dynamic process of droplets under linear shear was studied, and the influence of the effective capillary number (Cae) and the solid surface wettability on the deformation of clean droplets and surfactant-laden droplets was analyzed. The results show that the increase of the effective capillary number Cae promotes droplet deformation, but when it reaches a certain value, the droplet will rupture. While, surfactant-laden droplets exhibit the greater deformation and the movement speed compared to pure droplets. When droplets are attached to hydrophilic solid surfaces, they are further elongated under shear, exhibiting longer relative arc length and relative wetting length compared to neutral surfaces, while surfactant-laden droplets have longer relative arc length and relative wetting length compared to pure droplets. However, when droplets are attached to hydrophobic solid surfaces, they will detach from the solid surface under shear, and surfactant-laden droplets detach earlier than pure droplets. The research results indicate that the presence of soluble surfactants has a significant impact on the shear motion of droplets, promoting droplet deformation and increasing droplet movement speed. The numerical methods used in this study can be applied to calculate the moving contact line problem of droplets with soluble surfactants.