The Oblique Detonation Wave Engine (ODWE) may act as a hypersonic propulsion system operating at high Mach numbers, which is an important member in the family of Scramjet. Hydrogen is a promising fuel for Scramjet, which provides wider Mach number range and is environmentally friendly. The geometry of the engine greatly affects the performance of the ODWE using hydrogen fuel. This investigation focuses on a novel wedge proposed recently, which may be utilized in scramjet engines. The wedge consists of two sub-wedges and a step. This research focuses on how the geometry of the wedge affects the initiation characteristics of the oblique detonation. Simulations are conducted on basis of Euler equations and a 9-species and 19-reactions mechanism. It is found that a larger leading wedge angle leads to a shorter initiation length. A larger step angle induces a longer initiation length. Few effects are observed on the initiation characteristics for the current range of depth. The streamline surface at the rear of the step weakens the rear shock wave and induces a longer initiation length. The streamline surface at the tip of the step begins to take effect when the initiation position is away from the step. This research provides basis for understanding the performance of the oblique detonation wave under different geometries and provides theoretical basis for scramjet engine design. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.