To understand the phenomena of laminar diffusion flame along vortical walt, the numerical analysis has been performed. Keller-box method was used to solve the problem in the boundary layer. The governing equation is simplified by thin-flame approxiamtion. And energy and chemical species equations are normalized with Schvab-Zeldovich variables. A physical domain is divided the boundary layer along streamwise coordinate as the combustion region and the propagation region. And Radiation model is concerned in these region. As a result, typical phenomena have been observed. Comparison of the numerical results with experimental data shows that the present method can successfully predict phenomena of laminar diffusion flame along upright surface.