A heating method based on double-beam carbon dioxide (CO₂) laser is proposed, and the fabrication system of a long-period fiber grating with a microtapered structure is designed and built. The system achieves uniform heating and fiber softening by accurately controlling the CO₂ laser power, heating time, and spot size. The microtapered long-period fiber gratings (MT-LPFGs) with high-precision (extinction ratio >30 dB and insertion loss <1 dB) and without spectral degradation are fabricated by controlling the micro taper length and tapering ratio via a high-precision stepping motor. Based on cascaded MT-LPFGs, a broadband all fiber filter is realized. Experimental results show that the designed dual cascaded MT-LPFGs can achieve 15 nm broadband filtering at the extinction ratio of 30 dB, and the filtering bandwidth is increased by 7.5 times compared with that of the single grating. The three cascaded MT-LDFGs can achieve 25.2 nm broadband filtering at -25 dB band stop depth, which is 12.6 times that of a single grating. Finally, the bending tolerance of the cascaded grating filter is proved to be 1.183 m ^-1 by the bending experiment. The filter has advantages of high precision, simple preparation, and no spectral degradation, so it has an important application in broadband filtering.