The earthquakes could induce ionospheric electron density disturbance at D/E, F layer and even topside of ionosphere. Subsequently the ionospheric disturbance would change the electromagnetic field from the ground based VLF transmitter. Nowadays, the electromagnetic field recorded by Low earth orbit (LEO) satellite have been used to study the possible seismic anomalies frequently. It is essential to study systematically how the ionospheric disturbance influences the electromagnetic field at the altitude of LEO satellite theoretically. In this paper, we construct a full wave model to simulate the influence of the amplitude, altitude, and scale of the ionospheric disturbance on the electromagnetic field in the ionosphere from the ground based VLF transmitter. The result shows the electromagnetic field at the altitude of satellite changes obviously when the wave encounters an ionospheric disturbance in the D/E layer. The variation of the electromagnetic field increases with the amplitude and scale of the ionospheric disturbance. However, the influence of the ionospheric disturbance in the F layer just has a local effect on the electromagnetic field. The influence of ionospheric disturbance in the nighttime on the variation of electromagnetic field is smaller compared with it in the daytime. These conclusions can improve our understanding of using electromagnetic field observed by satellite to study seismic anomalies.