The measurement of yarn tension has a direct impact on the product quality and production efficiency in the textile manufacturing process, and the surface acoustic wave (SAW) yarn tension sensor is a good option for detecting the yarn tension. For SAW yarn tension sensors, sensitivity is an important indicator to assess their performance. In this paper, a new type of SAW yarn tension sensor based on a simply supported beam structure is studied to improve the sensitivity of the fixed beam SAW yarn tension sensor. The sensitivity analysis method based on elastic beam theory is proposed to illustrate the sensitivity optimization. According to the analysis results, the sensitivity of the SAW yarn tension sensor can be greatly improved by using a simply supported beam structure compared to the s fixed beam structure. Moreover, from the calibration experiment, the sensitivity of the simply supported beam SAW yarn tension sensor is 2.5 times higher than that of the fixed beam sensor.