It is well known that there is a linear electro-mechanical coupling under equilibrium thermodynamics in certain crystalline materials with non-centrosymmetric structures. Since Kogan and Meyer published their seminal papers in 1960s[1, 2], people have gradually realized that an inhomogeneous electro-mechanical coupling also exists in insulating materials, which is often called flexoelectricity. The physical mechanism of flexoelectricity in solid crystalline dielectrics is well known and its phenomenological model can be derived from the electromechanical energy coupling under equilibrium thermodynamics, whereas flexoelectricity in liquid crystals is closely related to the geometrical asymmetry of mesogen molecules or the shape polarity but the relation between the flexoelectric coefficients and molecular structures is far from being understood. Theoretically, flexoelectricity in polymers is similar to that in liquid crystals, which is largely dependent on rotation of molecules; therefore, the flexoelectric responses of polymers are complicated and might be different under external perturbations, such as tensile stretching, bending, electric field poling, etc. In this report, we will discuss experimental observations of the giant direct flexoelectric effect in certain polyvinylidene fluoride (PVDF) films under tensile stretching conditions. Our experimental studies indicate that the physical mechanism behind flexoelectricity in polymers might be more complicated than the one proposed for solid crystalline dielectrics.