In order to predict the effect of swirl on the structure of concentric laminar jet diffusion flame, present study examined the effect of swirl on the flame characteristics by numerical numerical analysis through theoretical model. The theoretical model has been developed for the co-axial laminar jet flame such that the fuel and air are supplying with swirl through inner and outer co-axial tube respectively. For the parametric study, swirl number, Reynolds number of fuel and air and directions of swirl are chosen as important parametes. The results of study show that the flame with width and shorter length is formed by larger swirl number. The important factor of the flame shape is the recirculating zone formed around jet axis near the exit of nozzle. In case of weak swirl, the effect of directions of swirl is not appeared. However, for the strong swirl, the flame with shorter length are appeared in case of counter-swirl compared with the case of co-swirl.