Linear displacement is used for positioning and scanning, e.g., in robotics at different scales or in scientific instrumentation. Most linear motors are either powered by rotary drives or are driven directly by pressure, electromagnetic forces or a shape change in a medium, such as piezoelectrics or shape-memory materials. Here, we present a centimeter-scale light-powered linear inchworm motor, driven by two liquid crystal elastomer (LCE) accordion-like actuators. The rubbing overwriting technique was used to fabricate the LCE actuators, made of elastomer film with patterned alignment. In the linear motor, a scanned green laser beam induces a sequence of travelling deformations in a pair of actuators that move a gripper, which couples to a shaft via friction moving it with an average speed in the order of millimeters per second. The prototype linear motor demonstrates how LCE light-driven actuators with a limited stroke can be used to drive more complex mechanisms, where large displacements can be achieved, defined only by the technical constrains (the shaft length in our case), and not by the limited strain of the material. Inchworm motors driven by LCE actuators may be scaled down to sub-millimeter size and can be used in applications where remote control and power supply with light, either delivered in free space beams or via fibers, is an advantage.