At present, the traction force and traction speed of the drilling robot cannot be controlled. However, if the speed of the drilling robot is too high, the bit will be damaged because of the shock load. If the speed of the drilling robot is too low, the drilling efficiency will be very low. The existing control system and control algorithm of the drilling robot cannot meet the requirements of the drilling conditions. A control system of the weight on bit and the rate of penetration of the drilling robot was invented. On the basis, a dual-loop fuzzy proportional integral derivative (PID) control algorithm of the pressure difference and flow rate was proposed to control the weight on bit and rate of penetration. Furthermore, the simulation model of the dual-loop fuzzy PID control algorithm was established. It is found that the proposed dual-loop fuzzy PID control algorithm has the characteristics of small overshoot and good tracking. Furthermore, the correctness of the theory was verified by the experiments. The experiments show that the average amplitude of rate of penetration vibration by using adaptive PID controller is less than 50% of that of PID controller. The maximum weight on bit with the adaptive PID controller is only 45.94% of that of the conventional PID controller. The overshoot of the adaptive PID controller is only 24.07% of that of the conventional PID controller. At the same time, the vibration amplitude of the conventional PID controller is obviously larger than that of the adaptive PID controller. The proposed adaptive PID controller in this paper can effectively reduce the vibration of the bit. By reducing the vibration of the bit, the life of the bit can be extended. Finally, it is of great significance to realize the efficient and intelligent drilling process.