We demonstrate a mode-locked all-fiber Er-doped fiber laser using the structure of a step-index multimode fiber and a graded index fiber as a new saturable absorber (SA) based on nonlinear multimode interference. By bending the SA to a certain state, stable soliton pulses are obtained at a pump threshold of 65 mW. The oscillator generates soliton pulses at 1598 nm with a spectral bandwidth of 3.4 nm, 960 fs duration and a fundamental repetition rate of 9.789 MHz. The output power of 24 mW is achieved at the maximum pump power of 700 mW, corresponding to a single pulse energy of 2.44 nJ. To the best of our knowledge, this is the first time anyone has achieved the highest single pulse energy in a fiber laser with the SA at 1.5 mu m to date. Moreover, the impact of diverse mode field diameters of graded index fiber on mode-locking behavior will also be discussed.