The effect of concentration gradient on detonation re-initiation behavior in a bifurcated tube full of oxyhydrogen mixture is numerically studied by employing an OpenFOAM based solver DCRFoam. The Naiver-Stokes equations (NS) with detailed chemical kinetics are solved to model the detonation diffraction, quenching and re-initiation process. The results show that compared with the homogeneous case, the second reflection is the key to the successful re-initiation of the detonation in mixture with concentration gradient instead of the first one, because multiple transverse waves are generated during the second reflection. With steepening the concentration gradient, the number and intensity of the transverse waves decreases, leading to the cellular structure more irregular and the decrease of detonation velocity. After the second reflection, the interaction between the concentration gradient and the leading shock leads to the concentration gradient existing not only in the transverse direction but also in the longitudinal direction. The longitudinal concentration provides the earlier H-2 for the formation and propagation of transverse detonation. Also, the Mach stem front bends greatly, and the transition distance from regular reflection to Mach reflection increases with steepening the concentration gradient.