This study proposes a fiber Bragg grating (FBG) sensor based on a singlemode-multimode-singlemode tapered structure that can effectively increase strain sensitivity. The grating is located at the tapered-multimode fiber region. A multimode fiber has the advantages of large aperture, easy coupling, easy writing of gratings, and the ability to withstand large strain. The use of tapered-multimode fiber gratings for strain sensing provides high accuracy and sensitivity. We produce multiple sensors with different tapers by changing the stretched length of the multimode fiber. Firstly, a 1.7-cm-long multimode fiber is welded between two singlemode fibers. Then, the middle multimode fiber section is tapered to 0.8, 0.9, and 1.0 cm, respectively. Subsequently, a 7-mm-long Bragg grating is written on the side of the multimode fiber cone. Changes in external parameters, such as temperature and strain, are monitored by analyzing the change of the resonant wavelength in the reflection spectrum. The experimental results show that the strain detection range of the sensor is 0-960 με,the highest strain sensitivity of the sensor can reach 15.5 pm/με, and the temperature sensitivity is 10.5 pm/℃. Furthermore, the thinner the cone radius is, the more obvious the increase in strain sensitivity is. The strain sensitivity is considerably improved compared with that of the conventional FBG, and the temperature sensing characteristics remain unchanged; hence, the temperature-induced strain error is only 0.677 με/℃ without temperature compensation, which reduces the cross-sensitivity between strain and temperature.