The structure of $H_2$ diffusion jet flame with coflowing has been investigated numerically to know the behavior of H-atom near the nozzle lip. Especially multi-step reaction model has been applied with the elliptic type governing equation to include the effect of axial diffusion in the equation. To calculate the thermodynamic and transport properties of the various chemical species and mixture, CHEMKIN code package has been applied. To minimize the numerical divergence due to the stiffness of combustion problem analysis, we have adopted the 3-step solution procedure ; cold jet, irreversible 1-step, and reversible 4-step reaction model. We have concentrated on the behavior of H-atom near the nozzle exit plane and have ascertained the fact that the rapid diffusion velocity of H-atom is the major driving force of the behavior of diffusion jet flame near the nozzle lip.