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For given incident plan waves,the scattered wave outside of an obstacle is governed by the Helmholtz equation in frequency domain.The inverse scattering problems aim to detect the obstacle property such as boundary shape and type from some information about the s cattered wave.In the case that the obstacle boundary is of impedance type,the inverse scattering problems need to identify both the bound ary shape and the boundary impedance simultaneously.In this talk,we will introduce our recent works for inverse scattering problems of an obstacle with impedance boundary.We will present the reconstruc tion schemes and show some influence of the impedance distribution on the shape reconstruction performance.Numerical implementations are also given.