The origami structure has attracted much attention due to its good folding characteristics and large folding ratio. The continuous robotic arm based on origami principle has also shown its advantages. However, how to retain the high foldability and flexibility of an origami robot while maintaining the rigidity and functionality of a articulated robot is always a challenging problem, especially in complex medical applications. This study proposes a medical robot based on an improved water-bomb origami continuum, which enables the robot to have good flexibility, high degree of freedom and high rigidity at the same time. In this study, the folding principle of the improved 8-fold water-boom origami was studied by combining the truss method and singular value decomposition method, and the motion model was established based on the kinematics of the continuum mechanism. Physical experiments involve redundant degrees of freedom and stiffness to thoroughly verify the motion model and performance of an origami continuum robot. The results show that the origami continuum robot can move freely in many forms in a complex environment.