Considering the devastating effects of near-fault earthquakes, seismologists and engineers have, qualitatively and quantitatively, represented the strong velocity Pulse of near-fault ground motions using models including physical parameters associated with the wave propagation process. In some mathematical models, the derivation of physical parameters is required to fit time history and response spectrum of the simulated record to the actual record through trial and error process, which limits the scope of these models. In the current study, the particle swarm optimization (PSO) algorithm is replaced with the trial and error procedure. In this way, an automatic and quantitative process with the minimal judgment of the analyst is prepared to extract a wide range of Pulselike records. Then, the proposed approach is applied to simulate and represent mathematically a set of 91 Pulselike records from the Next Generation Attenuation (NGA) project ground motion library. The obtained results show that a velocity Pulse of each Pulselike record could be extracted using the proposed approach, and it can therefore be considered as a powerful tool in Pulse parametric studies and the relationship between velocity Pulse and structure’ s response.