Nested multilayer mirrors are commonly used in X ray telescope structure to increase the collecting area. To balance the difficulty and cost of producing these mirrors, Wolter-I structures are replaced with conical Wolter-I structures, but these can lead to significantly poorer angular resolutions. In this Letter, we consider changing one of the mirror shapes (paraboloid or hyperboloid) of a Wolter-I structure to a conical mirror shape, while the other mirror shape remains a quadric surface-type structure, which can thus ensure the imaging quality. The cone-hyperboloid structure is nested to obtain on-axis angular resolution and off-axis images.