We created an all-fiber solution for fast, continuous, and controllable tuning of Fano-like resonance. By embedding a graphene-coated fiber Bragg grating into one arm of a Mach–Zehnder interferometer, the narrow Bragg resonance interacts with a broad interference spectrum, forming a sharp asymmetric Fano-like resonance line shape. With the application of an electrical voltage over the graphene layer, the generated Joule heating shifts the Bragg resonance and consequently tunes the asymmetric Fano-like resonance line shape to a symmetric dip or electromagnetically induced transparency-like peak. Further, by exploiting two modulated states with reversed Fano-like resonance line shapes, an optical switch can operate with an extinction ratio of 9 dB. The well-engineered Fano-like resonance in an all-fiber structure opens up new horizons for applications of fiber gratings in optical signal processing, slow-light lasing, and fiber sensing.