Flexoelectricity is a type of ubiquitous and prominent electromechanical coupling, pertaining to the response of electrical polarization to mechanical strain gradients while not restricted to the symmetry of materials. However, large elastic deformation in most solids is usually difficult to achieve and the strain gradient at minuscule is challenging to control. Here we exploit the exotic structural inhomogeneity of grain boundary to achieve a huge strain gradient (~ 1.2 nm-1) within 3 ~ 4 unit-cells, and thus obtain atomic-scale flexoelectric polarization up to ~ 38 {mu}C/cm2 at a 24 LaAlO3 grain boundary. The nanoscale flexoelectricity also modifies the electrical activity of grain boundaries. Moreover, we prove that it is a general and feasible way to form large strain gradients at atomic scale by altering the misorientation angles of grain boundaries in different dielectric materials. Thus, engineering of grain boundaries provides an effective pathway to achieve tunable flexoelectricity and broadens the electromechanical functionalities of non-piezoelectric materials.