A seismic wavelet parametric model was developed based on auto-regressive and moving average (ARMA) model theory. The model parameters were accurately determined based on cumulant fitting method. So the seismic wavelet can be a multi-parameters, multi-extremes nonlinear functional optimization problem. An improved particle swarm optimization with adaptive parameters and boundary constraints was proposed for the local extreme value defects of elementary particle swarm optimization. The optimization accuracy and computation efficiency are also improved. Simulation results show that the method has good applicability and stability in seismic wavelet extraction.