This paper presents a bending propagating actuation using SMA (Shape Memory Alloy) spring for an effective shape transition of a flytrap-inspired soft morphing structure. The flytrap-inspired soft morphing structure is made from unsymmetric CFRP (Carbon Fiber Reinforced Prepreg) structure which shows bi-stability and snap-through phenomenon. For a thin and large curved bistable CFRP structure, SMA spring is more acceptable than SMA wire and piezoelectric actuator which used in previous investigations. A bending propagating actuation is proposed which can induce snap-through of the bi-stable CFRP structure effectively. From this research, effective shape transition of soft morphing structure is possible.