A novel and reliable method enabling to produce an ultra-broad edge-filter (UBEF) is firstly proposed and demonstrated both theoretically and experimentally, which is realized by using a periodically-twisted graded-index few-mode fiber (GI-FMF). By using the proposed method, an UBEF with a dynamic wavelength-range up to ∼380 nm is numerically obtained. Furthermore, an UBEF with a linear dynamic range larger than ∼300 nm in wavelength and ∼12.7 dB in power was successfully demonstrated in experiment, which represent the highest performances among all those achieved from the fiber-based optical edge-filters (OEFs) reported to date. The proposed UBEF can be used as an ultra-broadband power interrogation component to well demodulate the wavelength-dependent signal, meanwhile it can be used as a highly-sensitive power-interrogated sensor as well. As typical application example of the proposed UBEF, a power-interrogated temperature sensor has been successfully demonstrated. The temperature responsivities with respect to the power change and the spectral shift are 0.0179 dB/°C and ∼0.49 nm/°C, respectively. The UBEF-based power-interrogated sensing system has the advantages of fast response, low cost, small size and high reliability.