Oblique detonation wave (ODW) in a non-uniform mixture was investigated using a two-stage light gas gun through a high-speed Schlieren photography. The concentration gradient was formed with hydrogen injection and controlled by the waiting time. Helium was used instead of hydrogen to measure the gradient by gas sampling. As the results, asymmetric curved ODW front appeared due to variable Chapman-Jouguet (C-J) speed. Asymmetric Straw-Hat type structure was also observed depending on the waiting time in which stabilized/attenuated ODW accompanied Straw Hat type structure above/below the projectile. Comparison to the cases of the uniform mixtures also revealed that the range of equivalence ratio for which ODW can be observed increases in the far field due to the absence of attenuation by the curvature effect and expansion wave, indicating that the criterion based on non-dimensional diameter is not always valid. In addition, one low-speed experimental case encountered a locally propagating detonation in a fuel-richer region, which can be attributed to a locally larger C-J speed exceeding the projectile speed.