||Inverse mean curvature flow have been studied not only as a geometric flow but also for applications to prove geometric inequalities like Riemann-Penrose inequality, Minkowski type inequality, etc. Analyzing solitons of a geometric flow is a natural way to understand the flow. Examples of the homothetic and translating solitons of the inverse mean curvature flow in Euclidean space are provided. The incompleteness for the solitons are observed from several examples and then, the incompleteness of any translating soliton and homothetic solitons with restrict homothetic ratio can be proved by applying maximum principle. Their area growths are obtained.