In order to solve the problems of landing stability and motion continuity of jumping robots in complex or narrow unstructured terrain， a soft jumping robot driven by shape memory alloy （SMA） smart material is proposed in this paper. It has the advantages of light weight， small size， simple structure， and continuous motion. The symmetrical origami flexible body is designed to reduce landing vibration and maintain landing stability； the symmetrical double SMA spring antagonism system is used to realize the function of structural deformation alternation for energy storage and release. Based on the theoretical model of this robot in the jumping process， the influence of key structural dimensions on energy storage and jumping performance is studied. A prototype with 6 cm×4 cm×2.5 cm in size and 3.8 g in mass is designed and manufactured. The experimental results show that this robot driven by SMA achieves jump triggering and posture recovery， whose maximum jumping height and distance are 8.67 cm and 18 cm， respectively. This robot can adapt to different working surfaces. With the advantages of good jumping ability and simple control sequence， this design lays a foundation for reconnaissance and detection work in unstructured terrain.