［Purposes］The interior inverse scattering problem with a mixed boundary condition is widely used in nondestructive detection. ［Methods］From the scattered wave generated by the point source located on the closed curve inside the cavity, the reciprocity gap functional is constructed based on the reciprocity gap method, the position and shape of the cavity are determined according to the norm property of the interaction gap functional. ［Results］It is proved that the solution of interior inverse problem with a mixed boundary condition is unique and the reciprocity gap functional is injective and dense. ［Conclusions］The position, shape and boundary impedance function of unknown cavity can be uniquely determined from the measurement data.