We present a robust chirped and tilted fiber Bragg grating (CTFBG) in a large-mode-area double-cladding fiber (LMA-DCF) written by a femtosecond (fs) laser. By implementing the fs-CTFBG into the output end of a high-power fiber laser for Raman filtering, a power handling capability of 4 kW is achieved with a Raman filtering ratio of ∼13 dB. To the best of our knowledge, this is the maximum handling power of a CTFBG for Raman filtering. The signal loss of the fs-CTFBG is 0.03 dB, which has little effect on the output laser beam quality. The air-cooled fs-CTFBG has a minimum temperature slope of 7.8°C/kW due to a self-annealing effect. This work proves the excellent performance of the fs-CTFBG, promoting the development of high-power CTFBGs.