Following the theory of evolutionary power spectral density for nonstationary processes, the formula of the time-varying auto regressive moving average (ARMA) model, referred to as TARMA, have been derived to simulate nonstationary downburst wind velocity. The simulation of nonstationary downburst wind velocity time history at some space points was carried out using TARMA. By resorting to Empirical Mode Decomposition (EMD) and the particle swarm optimization (PSO) based least squares support vector machines (LSSVM) as well as programming through MATLAB, the prediction of nonstationary downburst wind velocity time history at the middle space points was then accomplished through the nonstationary downburst wind velocity samples at the upper and lower two space points. It has been corroborated that the TARMA and EMD-PSO-LSSVM algorithm based simulation and prediction is feasible for nonstationary downburst wind velocity, through the comparison of the simulated and target values corresponding to the power spectrum, autocorrelation and cross-correlation functions, respectively.