We demonstrate an all-fiber ytterbium (Yb)-doped mode-locked oscillator using a hybrid structure based on no-core fiber graded-index multimode fiber (NCF-GIMF) as the saturable absorber (SA). The proposed SA exhibits unique characteristics such as large-power tolerance, high modulation depth of 24.7%, and low saturation intensity of 11.01 MW/cm2, which help to achieve a stable mode-locking operation. The all-normal and self-starting oscillator generates stable ultrafast pulses with a repetition rate of 21.35 MHz, pulse energy/average output power of 120 pJ/2.7 mW, and a pulse duration of 2.4 ps at a central wavelength of 1034.2 nm. The output pulses are then dechirped to 300 fs using an external grating compressor and possess high stability with a radio frequency spectrum of 58 dB. These results show that the NCF-GIMF-based SA can be used as an effective photonic device for high energy wave breaking free pulse generation. © 2020 Optical Society of America