A connecting structure connecting a first device and a second device rigidly but readily demountably comprises a housing having a top cover and a bottom cover to form an internal space. A connector which has an engagement block, a sliding block, and an insert block engages with the second device. A push button having a knob movably mounted on the housing, a sprung hooking structure having a guiding slot engaging with the sliding block, and a hook engaging with the second device provide demountable. The push button resists the engagement block via a through hole of the top cover, the connecting structure being combined with the connector to link with the hooking structure.