With the increasing output power of the monolithic fiber laser oscillators, the stimulated Raman scattering (SRS) effect becomes one of the main limitations of power scaling. Employing fiber with a larger mode area is an effective technique to mitigate the SRS, but, for the monolithic fiber laser oscillators, the difficulty of the inscription of the high-reflection fiber Bragg gratings (FBGs) increases with the fiber mode area. In this work, we demonstrated a high-power monolithic fiber laser oscillator based on the home-made large mode area FBGs and ytterbium-doped fiber (YDF) with 25 μm core diameters. A maximum output power of 4.05 kW is achieved at the central wavelength of ～1080 nm with a total 915 nm pump power of ～6.7 kW. At the operation of 4.05 kW, the intensity of the Raman Stokes light is ～25 dB below the signal laser, and the beam quality (M2-factor) is ～2.2. To the best of our knowledge, this is the first detailed report of the monolithic fiber laser oscillator with an output power beyond 4 kW.