A new type of drilling robot driven by drilling fluid is proposed, whose traction force is provided by differential pressure inside and outside of the drilling robot. The fluid mechanical model of differential pressure is established based on the principle of pressure drop. The equations for calculating the traction force of the robot in no-load condition and load condition are derived respectively. The dynamic model of drilling robot is established and the calculation method of key parameters such as weight on bit (WOB) and rate of penetration (ROP) in the dynamic model is derived. The influence of flow rate of drilling fluid on ROP/velocity and traction force of the drilling robot is analyzed. Among them, with the increasing of flow rate, the ROP/velocity and the traction force of drilling robot increases in a nearly linear trend. In the no-load condition (traction process), the drilling robot will be in acceleration until the telescopic cylinder stops pumping drilling fluid. In the load condition (drilling process), the drilling robot will reach a balance with the mechanical drilling rate within 0.1s. The proposed drilling robot can provide the possibility for the downhole operations in horizontal well with long displacement or in the condition of large traction force request. What’s more, this paper will provide a theoretical guidance for the control of ROP and WOB in the drilling process, and promote the application of drilling robots.