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In this paper, we propose and experimentally demonstrate a simple technique to enhance the curvature sensitivity of a bending fiber optic sensor based on anti-resonant reflecting optical waveguide (ARROW) guidance. The sensing structure is assembled by splicing a segment of capillary hollow-core fiber (CHCF) between two single-mode fibers (SMF), and the device is set on a steel sheet for measuring different curvatures. Without any surface treatment, the ARROW sensor exhibits a curvature sensitivity of 1.6 dB/m−1 in a curvature range from 0 to 2.14 m−1. By carefully coating half of the CHCF length with polydimethylsiloxane (PDMS), the curvature sensitivity of the ARROW sensor is enhanced to −5.62 dB/m−1, as well as an increment in the curvature range (from 0 to 2.68 m−1). Moreover, the covered device exhibits a low-temperature sensitivity (0.038 dB/°C), meaning that temperature fluctuations do not compromise the bending fiber optic sensor operation. The ARROW sensor fabricated with this technique has high sensitivity and a wide range for curvature measurements, with the advantage that the technique is cost-effective and easy to implement. All these features make this technique appealing for real sensing applications, such as structural health monitoring.