This article proposes a stochastic model for generation of synthetic seismic ground motions. In the first step, the wavelet coefficients of a record are extracted by the dual-tree complex discrete wavelet transform (DT-CDWT) and then they are simulated by an optimized Cauchy-Gaussian blend (CGB) model. This model predicts well the energy distribution of seismic ground motions, because in this model, the Gaussian distribution simulates smooth peaks and the Cauchy distribution is used to simulate impulsive peaks. Also, this model simulates several ascending-descending cycles in the time domain, predicts multiple frequency peaks each time, and simulates sequence-type records.