A small arbitrary walking and jumping actuator with a composited structure and size of 7 cm × 4 cm × 2.5 cm and mass of 5 g is proposed. An origami structure of polyvinyl chloride (PVC) membrane is designed for the main soft body, driven by shape memory alloy (SMA) springs and piezoelectric bimorphs. It has jumping, linear, and rotating motion modes. A simplified multi-faceted model by MATLAB software is established to perform a numerical analysis of the dynamics of jumping motion. Calculated results show that the length of the elastic belts have a directly proportional impact on the takeoff velocity, jumping legs orientation angle, shape and size of the body and air drag variably impact the jumping performance. The measured results show that the jumping height and distance are 10.3 cm and 19.8 cm, respectively, with a response time of 6.7 s at 1.4 A. The maximum rotating speed on the sandpaper and flat worktop are about 100 deg/s and 300 deg/s respectively. Its linear speed is more than 10 cm/s. • A small arbitrary walking and jumping actuator with composited structure is proposed. • A simplified multi-faceted model of jumping motion is established. • This actuator can jump and recover without motion failure.