Numerical simulation of an axisymmetric ethylene-air jet diffusion flame has been carried out in order to investigate flame dynamics and soot formation. The model solves the time-dependent Navier-Stokes equations and includes models for soot formation, chemical reaction, molecular diffusion, thermal conduction, and radiation. Numerically FCT(Flux Corrected Transport) and DOM(Discrete Ordinate Method) methos are used for convection and radiation trasport respectively. Simulation was conducted for a 5 cm/sec fuel jet flowing into a coflowing air stream. The maximum flame temperature was found to be approximately 2100 K, and was located at an axial position of approximately 5 cm from the base of the flame. The maximum soot volume fraction was about $7{ imes}10^{-7}$, and was located within the high temperature region where the fuel mole fraction ranges from 0.01 to 0.1. The buoyancy-driven low-frequency(12~13 Hz) structures convected along the outer region of the flame were captured. In case without radiation trasport, the maximum temperature was higher by 150 K than in case with radiation. Also the maximum soot volume fraction reached about $8{ imes}10^{-6}$. As the the hydrocarbon fuel forms many soot particles, the radiation transport becomes to play a more important role.