Biological muscles are multifunctional actuators that can change their stiffness and damping, and multipurpose variable stiffness actuators are designed to improve physical robotic interactions by giving variable stiffness actuators more capabilities and greater safety. In this paper, a novel design called Variable Stiffness Continuum Actuator (VSCA) is proposed by combining a pneumatic artificial muscle with the variable stiffness technique of the layer jamming principle. The VSCA not only has the function of a pneumatic artificial muscle capable of outputting high contraction force, but also is endowed with the ability to control the bending shape as well as the stiffness variation. A mathematical model of the VSCA’s output force is developed using the energy conservation principle. Quasistatic experiments, that include performance testing on the stiffness, contraction force, and variable stiffness of the VSCA, are carried out to confirm that the VSCA is stiffer than traditional PAMs and capable of achieving stiffness variations at varied vacuum levels. A lumbar spine-assisted therapy exoskeleton robot is designed to aid the elderly with lumbar rehabilitation activities using the VSCA’s mechanical features.