Pipe belt conveyor is a new type of environmentally friendly and efficient bulk conveying equipment. In the design of the roller, the belt and the driving motor of pipe belt conveyor, the sag resistance is a key parameter. Meanwhile, the normal force between the conveyor belt and the roller group is the other important factor need be considered and has a great influence on the sag resistance. This paper analyzes a pipe belt conveyor with a diameter of 150 mm to study the calculation method of normal force. And the relationship between the normal force and the sag resistance is explored. Firstly, the normal force is decomposed into three components related to the forming force of belt, material gravity and belt gravity. So it can be expressed as a linear combination of these three quantities, and the coefficients of each component are obtained based on the dynamic analysis of belt-roller. The results show that the coefficient is mainly affected by the material filling rate, and is almost not affected by the distance between the rollers and the density of the material. The calculation method of the normal force is eventually obtained. Secondly, the normal force in the case of different material filling rates is tested by experiments, and the calculation method of the normal force is verified. Thirdly, the variation law of the sag resistance in the case of different roller group spacing and material filling rate is studied by the dynamic model. It is found that the roller group spacing and material filling rate affects the sag resistance by changing the normal force. There is a power function relationship between the sag resistance and the normal force. In the case of different roller group spacing and material filling rate, the relationship among the sag resistance and the normal force remains unchanged. This study results are of great significance to the design of pipe belt conveyor.