In the simulation studied in this paper, the fifth-order upwind finite difference scheme and second-order Runge-Kutta method are used for the convective terms and the time developing term, respectively, in Navier-Stokes equations to simulate directly free air jet flow. The Reynolds number is 1200 and the calculated flow field ranges from the nozzle exit to the developed turbulent region. Since the computational cell size is smaller than Kolmogorov microscale in the developed region, calculated results can represent motions including micro-scale eddies. Calculated turbulent characteristics are compared with experimental results. Calculated results are in fairly good agreement with experimental data. The results show differences between high and low Reynolds number free jets. The calculated power spectra express experimental results, including high frequency spectra, well. Our computational visualizations show the unique phenomena of a low Reynolds number free jet, such as radial projecting eddies. It is concluded that the direct numerical simulation describes large-scale to micro-scale eddies in a low Reynolds number free jet, well.