A wheel drive mechanism is simple, stable, and efficient, but its mobility in unstructured terrain is seriously limited. Using a deformable wheel is one of the ways to increase the mobility of a wheel drive robot. By changing the radius of its wheels, the robot becomes able to pass over not only high steps but also narrow gaps. In this article, we propose a novel design for a variable-diameter wheel using an origami-based soft robotics design approach. By simply folding a patterned sheet into a wheel shape, a variable-diameter wheel was built without requiring lots of mechanical parts and a complex assembly process. The wheel's diameter can change from 30 to 68mm, and it is light in weight at about 9.7g. Although composed of soft materials (fabrics and films), the wheel can bear more than 400 times its weight. The robot was able to change the wheel's radius in response to terrain conditions, allowing it to pass over a 50-mm gap when the wheel is shrunk and a 50-mm step when the wheel is enlarged.