This paper studies the magnetisation and ac magnetisation losses caused by a travelling magnetic wave on a single-layer YBCO thin film. This work provides thorough investigations on how the critical magnetic field gradient has been changed by the application of a travelling wave. Several conditions were studied such as zero-field cooling (ZFC), field cooling (FC) and a delta-shaped trapped field. It was found that the travelling wave tends to attenuate the existing critical magnetic field gradients in all these conditions. This interesting magnetic behaviour can be well predicted by the finite element (FEM) software with the E–J power law and Maxwell’s equations. The numerical simulations show that the existing critical current density has been compromised after applying the travelling wave. The magnetisation profile caused by the travelling wave is very different from the standing wave, while the magnetisation based on the standing wave can be interpreted by the Bean model and constant current density assumption. Based on the numerical method, which has reliability that has been solidly proven in the study, we have extended the study to the ac magnetisation losses. Comparisons were made between the travelling wave and the standing wave for this specific YBCO sample. It was found that by applying the magnetic wave of the same amplitude, the ac magnetisation loss caused by the travelling wave is about 1/3 of that caused by the standing wave. These results are helpful in understanding the general magnetism problems and ac magnetisation loss in the travelling magnetic wave conditions such as inside a high temperature superconducting (HTS) rotating machine, etc.