This paper presents a new type of muscle-like actuator, namely double-acting (DA) sleeve muscle actuator, which is suitable for the actuation of biologically-inspired and biomedical robotic systems, especially those serving human-assistance purposes (prostheses, orthoses, etc.). Developed based on the traditional pneumatic muscle actuator, the new DA sleeve muscle incorporates a unique insert at the center. With the insert occupying the central portion of the internal volume, this new actuator enjoys multiple advantages relative to the traditional pneumatic muscle, including a consistent increase of force capacity over the entire range of motion, and a significant decrease of energy consumption in operation. Furthermore, the insert encompasses an additional chamber, which generates an extension force when pressurized. As such, this new actuator provides a unique bi-directional actuation capability, and, thus, has a potential to significantly simplify the design of a muscle actuator-powered robotic system. To demonstrate this new actuator concept, a prototype has been designed and fabricated, and experiments conducted on this prototype demonstrated the enhanced force capacity and the unique bi-directional actuation capability.