Recently, there have been many researches about applications of origami to mechanical engineering, which realizes a 3D sturcture by folding a 2D plane material. With this simple manufacturing process, origami was even adopted by some roboticists as a way to build an entirely new robot with benefits in terms of cost, weight, and structural simplicity. In this paper, we propose a new type of a walking robot based on origami structure. Because all the components of the robot that generate gait motion are mechanically connected, it can actually walk forward with only a single actuator. We also showed the similarity of gait trajectories between a kinematic analysis and the actual gait motion measured by video tracking. This result proved the possibility of designing an origami-based robot with the identical gait trajectory as we plan.