At present, the drilling rig for deep seabed shallow strata is widely used in the exploration of ocean cobalt-rich crust resources and other fields, which not only can obtain solid core samples at a specific station, but the operation process is relatively safe. This paper mainly presents the structure and mechanism of mobile drilling rig in acquiring the seafloor cores (up to 1.5 m long). Based on the function of the AMESim software, the hydraulic propulsion system model of mobile drilling rig is established, which is the basis and core part of the mobile drilling rig. Moreover, the control methods of closed-loop and PID are respectively used to control the hydraulic propulsion system for simulation analysis. Through the comparison of simulation results, it is found that the PID control method is more convincing in verifying the design rationality of hydraulic propulsion system. In the simulation of the PID-controlled hydraulic propulsion system, the co-simulation technology of AMESim and Matlab/Simulink not only establishes the hydraulic model and control model, but also determines the relevant simulation parameters, which is helpful to improve the system simulation efficiency. In its verification deployment in the South China Sea, the mobile drilling rig has been operated for many times at different depths, and some cores have been successfully obtained. Furthermore, the mobile drilling rig has been used during the 55th Voyage of China Oceanic Scientific Expedition supported by China Ocean Mineral Resources R&D Association. Several sites were explored and a large number of cobalt-rich crust cores were obtained. The powerful theory and sea trails are provided to support for the further research on survey of the abyssal resource.