Origami provides a unique tool for the design of robotic frames owing to its simple shaping principle by "folding." However, achieving the fast and reversible activeness of a highly reconfigurable structure remains challenging owing to the limitations of accessible actuators. In particular, it is difficult to find an actuator that can realize a simultaneously large, rapid, reversible, and stable movement while leading to a favorable form factor for the origami. To overcome this, in this article, we propose a 3-D shape-shifting system consisting of a morphing origami block that complements the stability problem of shape memory alloy wire actuators by tuning its structural characteristics. This cooperative scheme improves the reversibility and stability of the shape-shifting system, which enables the rapid transformation with high degrees of freedom unlike in existing programmable origami. As a stand-alone unit of transformation, morphing block equipped with deployable mechanism and actuators weighs 6 g and has a volume change factor of ten. Furthermore, the transformation time in both directions is less than 5 s, and the block can carry more than 120 g of payload in the deployed state. The proposed system composed of multiple origami blocks can reconfigure itself into diverse 3-D target shapes.