Bouncing locomotion is used frequently in the animal kingdom for high speed movement over land. Animals also change their stiffness and shape to improve their locomotion ability. Both bouncing movement and stiffness- and shape-changing capabilities have been recently explored in robotics. In this paper a novel soft locomotion robot, VibroBot, is presented, capable of moving using a bouncing gait by inducing whole-body oscillations through rotation of an internal out-of-balance mass. VibroBot is capable of changing both its stiffness and shape to tackle challenging terrain and to overcome obstacles. When the robot is stiff, it is capable of high-frequency oscillatory locomotion suited to movement on hard surfaces, while in a compliant state it uses a lower-frequency higher-amplitude hopping gait suitable for travelling over soft or loose ground. Forward speeds of 8.5 cm/s (0.34 body lengths per second) on hard floor in VibroBot’s stiff state and 5 cm/s (0.2 body lengths per second) on sand in its compliant state were recorded. VibroBot can also selectively change its shape to climb obstacles with heights up to 3 cm (20% of the robot’s height in its stiff state), far greater than its hopping apex height (1 cm). Both simple bouncing gaits and stiffness- and shape-changing abilities show great promise for improving the locomotion abilities of soft robots.