In response to the problem of low sensitivity of bare fiber Bragg gratings to ultrasound, the article proposes a series of polymer encapsulated fiber Bragg grating sensors. By encapsulating a polymer coating layer aroud the gratings that is much thicker than the diameter of the fiber, the strain sensitivity of the fiber Bragg gratings under ultrasound action is improved. Firstly, a fiber grating sensing model is established, and the influence of polymer Young's modulus and Poisson's ratio on fiber grating strain is analyzed based on the transfer matrix method. And then, fiber Bragg gratings are encapsulated using three polymer materials with different parameters, namely polyurethane (PU), polyacrylate (ABR), and polyvinyl chloride (PVC). The wavelength drift of the fiber Bragg grating is converted into a voltage signal using linear edge filtering method, and the sensing characteristics of the encapsulated sensors for ultrasound are measured. The results show that the decrease of Young's modulus and the increase of Poisson's ratio of polymers are helpful to improve the sensitivity of fiber gratings to ultrasonic response. And among the three materials, PU packaging has the best effect, with a peak voltage of 139.6 mV, which is about 15 times that of the bare fiber gratings. In addition, the peak voltage of the packaged sensor decays exponentially with the increasing distances from the sound source, which conforms to the attenuation trend of ultrasound in water and can restore the sound field state in space.