Ship underwater radiated noise is one of the most important ocean ambient noise sources, and building a reasonable model for the ship underwater radiated noise is helpful for understanding the physical mechanism and reducing research cost of ship underwater radiated noise. The quasi-periodic random sound pulse sequence signals act well in explaining the rhythm and the power spectrum variation of the ship underwater radiated noise, and reveal that there are not any real sinusoidal components in ship radiated noise signals, which come from the non-linear transformation of the signals, and the analysis of some representative experimental data of ship radiated noise also supports this idea. Based on this, the explosion-type cosine pulses are used as the units of quasi-periodic random sound pulse sequences. This model can generate the power spectrum with a peak, and the peak location can change with ship velocity or ship type. The power spectrum variation characteristics of quasi-periodic random sound pulse sequences consisting of the explosion-type cosine pulses are in good agreement with the measured ship underwater radiated noise data, which shows that this model is of important practical value.