This paper presents a folded surface detection and tracking method for augmented maps. First, we model a folded surface as two connected planes. Therefore, in order to detect a folded surface, the plane detection method is iteratively applied to the 2D correspondences between an input image and a reference plane. In order to compute the exact folding line from the detected planes for visualization purpose, the intersection line of the planes is computed from their positional relationship. After the detection is done, each plane is individually tracked by the frame-by-frame descriptor update method. We overlay virtual geographic data on each detected plane. As scenario of use, some interactions on the folded surface are introduced. Experimental results show the accuracy and performance of folded surface detection for evaluating the effectiveness of our approach.