Surfactants can reduce fluid interface tension and significantly alter the wetting properties of solid surfaces, making them essential in various industrial applications. To investigate the motion characteristics of surfactant-laden droplets on solid surfaces, a coupled model incorporating soluble surfactant flow and contact line dynamics was established using the Cahn-Hilliard phase field lattice Boltzmann method, alongside the Yokoi dynamic contact angle model considering the velocity of the three-phase contact line based on experimental data. A computational program was independently developed and optimized with parallel processing to improve computational efficiency. Subsequently, the dynamic behavior of droplets under linear shear flow was studied, focusing on the influence of the effective capillary number (Ca_e) and surface wettability on the deformation of both clean and surfactant-laden droplets. The results show that an increase in the effective capillary number (Ca_e) promotes droplet deformation, but beyond a critical threshold, the droplet ruptures. Surfactant-laden droplets exhibit greater deformation and faster movement compared to pure droplets. On hydrophilic surfaces, droplets elongate further under shear, with surfactant-laden droplets exhibiting longer relative arc and wetting length than their pure counterparts. Conversely, on hydrophobic surfaces, droplets tend to detach under shear, with surfactant-laden droplets detaching earlier than pure droplets. These findings indicate that soluble surfactants significantly impact droplet shear dynamics by promoting deformation and increasing movement speed. The numerical methods presented in this study offer a robust approach for simulating moving contact line problems in droplets containing soluble surfactants.