A novel bidirectional high-sensitivity fiber-optic bending sensor based on the concave-lens-like long-period fiber grating (CLL-LPFG) is designed and demonstrated. The CLL-LPFG is composed by an array of arc-shaped grating planes, and accordingly, its refractive index modulation serves as a concave lens. As a result, the eigencladding mode of the device gets closer to the device surface than the conventional counterpart. Therefore, the proposed sensor provides a more sensitive result. The experimental results show that the bending sensitivities of the CLL-LPFG reach -32.782 nm/m-1 within the bending range of 0-2.08 m-1, which is about sixfold compared to the reported arts. The sensitivity can be potentially improved by optimizing the grating parameters, and the temperature characteristics of the CLL-LPFG can be used to manipulate the grating spectrum.