In this study, we propose a novel method for planning the folding process of a rigid origami mechanism, i.e., we explore the intermediate process of the mechanism from an initial state to a target state without self-intersection via a path-finding algorithm. A typical problem associated with a path-finding algorithm is that a feasible configuration space of rigid origami is a lower-dimensional subset of the entire parameter space. When all the folding angles are considered as free parameters to plan the folding process, it is generally not possible to obtain a feasible configuration via sampling. In this study, the parameters corresponding to the degree of freedom (DOF) are used as independent variables, and the remaining fold angles are considered as dependent variables that can be calculated via the explicit expression method (EEM). First, we explain the method for choosing the parameters related to DOF to represent the configuration of the origami mechanism. Then, we show the procedure for selecting a valid configuration from many possible configurations computed via EEM. For this purpose, we introduce criteria for each vertex to determine whether the two configurations can be continuously connected. Next, the method for planning the folding process of rigid origami is introduced via the rapidly-exploring random tree (RRT) method. Finally, we implemented the folding process simulation platform and applied it to different patterns. The results of the experiments are presented.