The characteristics of high-frequency (HF) electromagnetic (EM) wave propagation can be affected when EM waves propagate in the ionosphere. When ionospheric irregularities appear in the ionosphere, they can have a serious impact on the propagation of HF EM waves. In this study, the propagation of HF EM waves in ionospheric irregularities was investigated by numerical simulation. First, a two-dimensional model of plasma bubbles was used to produce ionospheric irregularities in the ionosphere. A ray-tracing method was then utilized to simulate the propagation of HF radio waves in these ionospheric irregularities. Results showed that the propagation of HF radio waves in the ionosphere was more complex in ionospheric irregularities than without ionospheric irregularities. In addition, corresponding ionograms were synthesized by radio rays propagated in the ionosphere with these irregularities. The synthesized ionograms were then compared with the experimental ionograms recorded by an ionosonde. Results showed that spread F could be simulated on the ionograms when ionospheric irregularities occurred in the ionosphere. This result was consistent with the ionosonde observations.