With the increasing demand for resources, the task of the geological survey is growing rapidly. The automatic geological drilling rig, which can improve the efficiency of the geological survey, has become the mainstream development direction. In this study, the hydraulic control system for the automatic screw up and screw down of an automatic drilling rig is studied. Through the establishment of mathematical models such as the four-way slide valve controlled asymmetric cylinder model, drill pipe thread stress model, and steel wire rope elastic model, the hydraulic valve is used to limit the pressure of the hydraulic cylinder, closed-loop control to control rotation speed, and power head floating to prevent screw damage and realize the automatic control of drill pipe up and down of a geological drilling rig. The hydraulic control system is simulated by AMESim software. The simulation model verifies the mathematical model. It is concluded that the maximum transient force of steel wire rope is caused by the elastic coefficient K of steel wire rope, but the magnitude is independent of K. The transient force is the periodic motion force. The displacement, velocity, and acceleration of load are periodic functions related to time. By installing a small flow load sensing valve, the displacement of an asymmetric hydraulic cylinder can be accurately controlled, and then, the displacement of the drilling rig powerhead can be controlled. The combined action of drill pipe speed and power head displacement is adopted, and the power head displacement is followed by PID control through the feedback value of the drill pipe speed, which can realize the automatic loading and unloading of drill pipe and reduce the damage of drill pipe screw during loading and unloading of drill pipe. The research results of this study can provide a theoretical reference and design basis for the follow-up development of an automatic drilling rig.