Rigid origami-based reconfigurable structures exhibiting multiple shapes have great potential applications for multifunctional devices such as antennae for multiple services of wireless communication. However, it is a challenge to design origami with reconfigurability. Here, a design method for the reconfigurable origami based on crease-duplicating and mountain-valley-setting is proposed, starting from a diamond origami pattern. By integrating the vertex-splitting technique with crease duplication, two reconfigurable origami patterns based on the transformation of creases between mountain and valley are created. Subsequently, the corresponding thick-panel forms are constructed by accommodating thickness to panels. The reconfigurability is achieved by introducing the kirigami technique. Then, kinematic analysis is carried out, which indicates the zero-thickness origami is kinematically equivalent to the thick-panel form. Furthermore, a reconfigurable antenna with three beamwidth characteristics is constructed based on one of the reconfigurable origami patterns and validated its performance through experiments. The design method of reconfigurable origami is beneficial for promoting the application of origami in multifunctional devices.