In recent years, fiber Bragg grating (FBG) strain sensors have been widely applied to measure strain and relative physical quantities. However, the direction of strain must be along the axial or transverse direction of FBG for many FBG sensors, significantly limiting application. Here, the sensing characteristics of FBG for different incident strain waves were determined, and the influences of the incident angle of static strain, low frequency strain, and high frequency strain on FBG sensitivity were characterized. The construction of an FBG strain sensor that can measure strain with any incident angle is proposed, and additional applications of sensing characteristics are discussed.