In this work, a SAW pressure sensor based on a simply supported beam was designed and fabricated. The SAW resonator deposited on 128° YX-lithium niobate (LNO) substrate was used as the sensing element. The LNO substrate was used as a simply supported beam, therefore strain transfer loss was avoided and uniaxial stress was directly applied to the SAW resonator. An indenter with two ledges was used to indent the LNO beam and then uniform strain was applied to the SAW resonator. The sensitivity was experimentally measured in a pressure range of 330 kPa. The results demonstrated that the sensitivity of the SAW pressure sensor in this work was as high as 2514 ppm/MPa. The high pressure sensitivity of the proposed SAW pressure sensor was analyzed. The device structure of the proposed SAW pressure sensor may help to design highly sensitive SAW pressure sensors.