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We investigate the controllability of an origami system composed of Miura-ori cells. A substantial volume of research on folding architecture, kinematic behavior, and actuation techniques of origami structures has been conducted. However, understanding their transient dynamics and constructing control models remains a formidable task, primarily due to their innate flexibility and compliance. In light of this challenge, we discretize the origami system into a network composed of interconnected particle masses alongside bar and hinge elements. This yields a state-space representation of the system's dynamics, enabling us to obtain the system's controllability attributes. Informed by this computational framework, we explore the controllability Gramian-based method for finding the most efficient crease line for Miura-ori cell deployment using an actuator. We demonstrate that the deployment efficiency guided by this theoretical method agrees with the empirical results obtained from the energy consumption to deploy the origami structure. This investigation paves the way toward designing and operating an efficient the complex actuation system for origami tessellations.