Characterizing fracture is important in order to understand how groundwater is transported and stored in fractured environments, to assess contaminant transport through fractures, as well to evaluate the mechanical behaviour of a fractured rock mass. In this research, we have investigated through careful laboratory experiments the amplitude versus offset (AVO) response of seismic reflections from a fracture. We use the linear slip boundary condition at the fracture and estimate the angle-dependent reflection response due to a single fracture. The observed angle-dependent reflectivity is inverted to obtain the fracture compliance and aperture. Two detailed laboratory experiments are performed - one using laterally homogeneous fracture and another using laterally heterogeneous fracture (partly air-filled and partly water-filled). Our results demonstrate that normal compliance (inverse stiffness) of a fracture can be quite accurately estimated from the AVO inversion of P-P reflected waves. It is also possible to obtain the non-zero tangential compliance. The existence of fluid in the fracture can be predicted. Distinction of the fracture infills and quantification of the fracture aperture are possible. This finding will be crucial for numerous new applications in civil and geotechnical engineering, hydrogeophysics, as well as in other areas of earth sciences and non-destructive material testing.