It transpires that the irregularity in the structure of the ionospheric plasma plays a significant role on the ionospherically-propagated HF signals. In this paper, special attention has been paid to derive a simulator that can explicate the perturbed phase influence imposed by the ionosphere irregularities. This has been achieved by studying the space-time correlation as well as statistics of the perturbed phases so that the problem of perturbed phase simulation is recast as generating particular time series satisfying specific power spectrum and statistical distribution. Eventually, three scenarios corresponding to different irregularity fluctuation conditions are considered to verify the effectiveness of the proposed simulator. It is shown numerically that the obtained perturbed phases can agree well with the theoretical assumptions.