This paper presents the design of a bio-inspired crawling robot comprised of bi-stable origami building blocks. This origami structure, which is based on Kresling origami pattern, expands and contracts through coupled longitudinal and rotational motion similar to a screw. Controlled snapping, facilitated by buckling instability, allows for rapid actuation as seen in the mechanism of the hummingbird beaks or the Venus flytrap plant, which enables them to capture insects by fast closing actions. On a much smaller scale, a similar buckling instability actuates the fast turning motion of uni-flagellated bacteria. Origami provides a versatile and scale-free framework for the design and fabrication of smart actuators and structures based on this bi-stable actuation scheme. This paper demonstrates how a bi-stable origami structure, having the geometry of a polygonal base prism, can be used to actuate crawling gait locomotion. Bi-stable origami structures exhibit buckling instabilities associated with local bending and buckling of their flat panels. Traditional kinematic analysis of these structures based on rigid-plates and hinges at fold lines precludes the shape transformation readily observed in physical models. To capture this behavior, the model presented utilizes principles of virtual folding to analyze and predict the kinematics of the bistable origami building blocks. Virtual fold approximates panel bending by hinged, rigid panels, which facilitates the development of a kinematic solution via traditional rigid-plate analysis. As such, the kinetics and stability of the structures are investigated by assigning suitable torsional springs' constants to the fold lines. The results presented demonstrate the effect of fold-pattern geometries on the chirality (i.e. the rotational direction that results in expansion of the structure), and snapping behavior of the bi-stable origami structure. The crawling robot is presented as a case study for the use of this origami structure in various locomotion applications. The robot is comprised of two nested origami 'building blocks' with opposite chirality, such that their actuations are coupled rotationally. A servo motor is used to rotationally actuate the expansion and contraction of both the internal and external origami structures to achieve locomotion. Inclined barbs that extrude from the edges of the polygonal base engage with the ground surface, thus constraining the expansion or contraction to forward locomotion, as desired. The robot fabrication methods are presented and results from experiments performed on various surfaces are also discussed.