This paper studies round jet with large eddy simulation (LES) method, in which spectral element technique is used as spacial discritization for the large eddy simulation Navier-Stokes equations. A local spectral discretization associated with Legendre polynomials is employed on each element of the structured mesh, which allows for high accurate simulations of turbulent flows. Discontinuities across the interfaces of the elements are resolved using a Riemann solver. An isoparametric representation of the geometry is implemented, with boundaries of the domain discretized to the same order of accuracy as the solution, and explicit low-storage Runge-Kutta methods are used for time integration. LES results of round jet are presented, in which the instantaneous and statistical turbulence structures of the round jet have been captured. The probability density function, and the spectral density function of the round jet that can reflect properties of turbulence have also been estimated. The work serves the purpose of allowing fast, convenient computations and comparisons with theoretical results and the ultimate goal is to develop it into an LES code featuring spectral accuracy with minimum dissipation and dispersion, a valuable tool for round jet computations.