This paper presents a bio-mimetic flytrap robot based on the Venus flytrap, which has rapid snap-through motion. The robot employs a bi-stable unsymmetrically laminated carbon fiber reinforced prepreg (CFRP) structure, which has a bi-stable mechanism that is similar to the Venus flytrap's passive elastic mechanism. By embedding shape memory alloy springs, large deformation is induced and bi-stable structure can be triggered to snap through. The robot's working performance shows that the leaves close in about 100ms, and this time for closure is almost the same as that of the Venus flytrap. This concept of the flytrap robot can be applied to rapid grippers of various sizes.