Origami has been intensively investigated due to its unique properties of changing designed planetary configurations to fit curved surfaces and compact forms. In this paper, the cylindrical origami structures based on generalized Miura-ori tessellations are studied, including geometric parameters, folding behaviors, and target curvature fitting. The design of the in-plane crease patterns to make the origami approximately fit a target cylindrical surface is first presented based on the out-of-plane method and parametric modeling. Multiple free parameters are undetermined while fulfilling the geometric constraints to realize this objective. Next, we systematically studied different folding behaviors and their resulting geometric patterns by varying these free parameters. Finally, methods are presented to locally modify the deployment kinematics while fitting the same target surface. This research extends the understanding of origami behaviors to full-period folding processes, which can be potentially applied in diverse engineering applications.