In the drilling industry, it is of great significance to accurately predict the drag coefficient and settling velocity of drill cuttings falling in the non-Newtonian drilling fluid. However, the irregular shape of drill cuttings and the non-Newtonian rheological properties of drilling fluid (e.g., shear-thinning and yield stress behavior) make it challenging to predict the settling velocity. In this study, the velocity of particle settlement was studied by a visual device and high-speed camera system. Experimental data of the free settlement of 224 irregular drilling cuttings and 105 spherical particles in the Herschel–Bulkley fluid were obtained. A mechanical model dependent on the force balance of settlement particles was adopted to conduct a detailed statistical analysis of the experimental results, and a prediction model of the drag coefficient of spherical particles in the Herschel–Bulkley fluid was established. A two-dimensional shape description parameter is introduced to establish a model for predicting the drag coefficient of irregular-shaped cuttings in a Herschel–Bulkley fluid. The model has high prediction accuracy for the settling velocity of irregular shale cuttings in Herschel–Bulkley fluid. The average relative error is 7.14%, verifying the model’s accuracy.