Electrothermally-driven carbon nanotube (CNT) fiber artificial muscles have attracted considerable interest in the fields of soft robotics, sensors, and intelligent control, owing to their excellent flexibility, abundant guest material sources, lightweight properties, rapid response, and ease of control. Nevertheless, their practical application has been impeded by the limited contractile stroke and contractile stress under high load conditions. Drawing inspiration from the physiological structure of muscle fiber, this study reports an endomysium-inspired-sheath artificial muscle (ESM). The ESMs are characterized by polydimethylsiloxane (PDMS) sheaths that mimick the endomysium, and multifilament cores made from CNT fibers imitating the myofibrils. The ESMs demonstrate excellent actuation performance, achieving maximum contractile stress of 40.1 MPa, the highest reported value among electrothermally-driven CNT fiber artificial muscles. The ESMs also demonstrate large contractile stroke and high work capacity under heavy loads. Furthermore, a crawling robot with the capacity of carrying loads, driven by a single ESM, is developed to demonstrate the practical application potential of ESMs.