We demonstrate an all-fiber mode locked laser based on hybrid structure of multimode fiber saturable absorber (SA) that can realize both conventional soliton and stretched-pulse states. Stable 16.44 MHz conventional soliton pulses are achieved by injecting 80 mW threshold pump power. By increasing the incident pump power to 420 mW, the laser evolves from soliton operation into stretched-pulse mode locking state. 310 fs stretched-pulse are obtained with the same repetition rate as the soliton pulses. The center wavelength and its 3 dB spectrum bandwidth are 1603 nm and 14.2 nm, respectively. For the first time, we experimentally confirm transition between conventional soliton and stretched-pulse in 1.5 μm mode-locked fiber laser by introducing multimode optical fiber SA. Moreover, the maximum single pulse energy of nearly 1 nJ is achieved. Such all-fiber mode-locked lasers based on hybrid structure of multimode fiber are attractive for practical applications without damage and the limitation of life time.