The low energy electronic structure of Sr2IrO4 has been well studied and understood in terms of an effective Jeff = 1/2 Mott insulator model. However, little work has been done in studying its high energy electronic behaviors. Here we report a new observation of the anomalous high energy electronic structure in Sr2IrO4. By taking high-resolution angle-resolved photoemission measurements on Sr2IrO4 over a wide energy range, we have revealed for the first time that the high energy electronic structures show unusual nearly-vertical bands that extend over a large energy range. Such anomalous high energy behaviors resemble the high energy waterfall features observed in the cuprate superconductors. While strong electron correlation plays an important role in producing high energy waterfall features in the cuprate superconductors, the revelation of the high energy anomalies in Sr2IrO4, which exhibits strong spin-orbit coupling and a moderate electron correlation, points to an unknown and novel route in generating exotic electronic excitations.