An electrically controllable fiber Bragg grating inscribed in a hydrogen-loaded standard single-mode fiber with liquid-crystal cladding is presented. Control of the optic axis of liquid crystals by means of external electric fields results in the change of reflectivity and Bragg wavelength of the grating. The increase of surrounding refractive index of a fiber makes effective refractive index of a propagation mode higher, which results in high field confinement and longer Bragg wavelength. The reduction of the fiber diameter by chemical etching process improves the long-range ordering of liquid-crystal molecules and reduces controlling voltage. The tunable ranges of reflectivity and Bragg wavelength of the liquid crystal-cladding fiber Bragg grating were $~4.6dB;and;~0.3nm$, respectively.