In this paper a new rotary position sensing structure based on a pair of fiber Bragg gratings (FBGs) is experimentally demonstrated with capability of detecting rotating angle of a rotor which is rotated in arbitrary direction or rotated in the same direction infinitely. Moreover, owing to its miniature size, this structure can also be used for small rotary apparatus as a tiny rotating position sensor. The operation mechanism is mainly based on the difference between the wavelength shifts of two FBGs respectively due to the axial strain caused by bending the cantilever towards the angular direction corresponding to the rotating position of rotary shaft. A deviation of 1.1 degrees for rotary angle detecting is obtained.