Oblique ionogram inversion is an important tool for understanding the ionosphere. Vertical plasma density profiles are the most common inversion results for the majority of the inversion algorithms. However, the inversion of the dynasonde ionogram provides not only the vertical plasma density profile, but also two tilts profiles directly related to the horizontal gradients of the plasma density. The main reason is that the dynasonde ionogram inversion uses a 3D numerical ray-tracing technique that considers the geomagnetic field and the horizontal inhomogeneity of the ionosphere. The theory and the ray-tracing performance of the 3D numerical ray-tracing method are presented. The ray-tracing method uses a variable-step strategy to speed up the simulation. And three plasma density models with traveling ionospheric disturbances and small-scale irregularities and without them are considered when using the presented ray-tracing method to simulate oblique ionograms. The simulation results show that the ionosphere disturbances can eventually be embodied in the simulated oblique ionograms.