We consider the initial-boundary value problem of the wave equation with space-dependent damping in an exterior domain. We give energy estimates and asymptotic profiles of solutions with polynomially decaying initial data. The proof is based on the energy method with suitable weight functions which behave like polynomials at the spatial infinity. To construct these weight functions, we introduce suitable supersolutions for the corresponding parabolic equation by using Kummer's confluent hypergeometric functions. This talk is based on a joint work with Prof. Motohiro Sobajima(Tokyo University of Science).