In this study, numerical simulations using Euler equations with detailed chemistry are performed to investigate the effect of fuel-air composition inhomogeneity on the oblique detonation wave (ODW) initiation in hydrogen-air mixtures. This study aims for a better understanding of oblique detonation wave engine performance under practical operating conditions, among those is the inhomogeneous mixing of fuel and air giving rise to a variation of the equivalence ratio (ER) in the incoming combustible flow. This work focuses primarily on how a variable equivalence ratio in the inflow mixture affects both the formation and characteristic parameters of the oblique detonation wave. In this regard, the present simulation imposes initially a lateral linear distribution of the mixture equivalence ratio within the initiation region. The variation is either from fuel-lean or fuel-rich to the uniform stoichiometric mixture condition above the oblique shock wave. The obtained numerical results illustrate that the reaction surface is distorted in the cases of low mixture equivalence ratio. The so-called "V-shaped" flame is observed but differed from previous results that it is not coupled with any compression or shock wave. Analyzing the temperature and species density evolution also shows that the fuel-lean and fuel-rich inhomogeneity have different effects on the combustion features in the initiation region behind the oblique shock wave. Two characteristic quantities, namely the initiation length and the ODW surface position, are defined to describe quantitatively the effects of mixture equivalence ratio inhomogeneity. The results show that the initiation length is mainly determined by the mixture equivalence ratio in the initiation region. Additional computations are performed by reversing ER distribution, i.e., with the linear variation above the initiation region of uniform stoichiometric condition and results also demonstrate that the ODW position is effectively determined by the ER variation before the ODW, which has in turn only negligible effect on the initiation length. (C) 2017 Elsevier Masson SAS. All rights reserved.