Soft linear actuators have strong deformation ability and good environmental adaptability, which have been widely used in soft robot design. However, little work has focused on designing soft linear actuators with balanced performances, featuring fast driving speed, large output displacement, being lightweight, and miniaturization. Herein, we present a novel soft linear actuator design based on the Kresling origami structure. By driving the Kresling tubes with a servo motor, the soft linear actuator has good compliance and strong environmental adaptability and can achieve a driving speed, large driving force, and high control precision comparable to the traditional electrical motor. The analytical models of the Kresling tubes and the whole actuator are respectively derived to analyze the mechanical properties, determine the optimal geometry of the Kresling tube, and evaluate the driving performance of the whole actuator. The actuator prototype is fabricated by 3D printing, and the actual driving performance is tested. It is shown that the prototype can achieve a maximum output displacement of 18.9 mm without payload or 16 mm under a payload of 30 N. Finally, as a case study, the soft linear actuator is applied to a crawling robot, where the maximum moving speed of 28 mm/s is reached.