There are many difficulties to get the scattered field generated by obstacle which has arbitrary shape or irregular surface impedance by using analytic solution or numerical methods. In this study, we propose a method of which makes acoustic scattering holography that can predict the far-field scattered field based on nearfield measurements. This method provides the scattered fields of each wave-number components of incident fields. We express the relationship of wave-number components between incident fields and scattered fields using scattering matrix which is transfer matrix of wave-number components. Lastly, we prove the relation between wave-number components of incident and scattered field by experiments. The errors which are caused by measurements and decomposition methods are also analyzed.