We present a spectrum-tunable fiber Bragg grating (FBG) based on a unique compress-twist deformation mode of non-rigid origami. By applying axial displacement on the FBG-bonded Kresling-ori, a non-uniform strain field emerges. The mechanics-induced non-uniform strain can shift the wavelength of an apodized unchirped FBG and/or transform an apodized unchirped FBG to a chirped one. For the spectrum-shaping mode, the bandwidth of the FBG was tuned from 0.32 nm up to 2.9 nm, measured at the -6dB level. For the wavelength-shift mode, a maximum wavelength shift of 0.6 nm can be achieved.