Illex argentinus is a short-lived cephalopod species, which is also a commercially important species in the world. The Malvinas Islands is one of the important fishing grounds for Illex argentinus. The abundance of Illex argentinus is highly susceptible to marine environmental changes and has large interannual fluctuations. According to the statistical data of Illex argentinus in the Malvinas Islands from 1995 to 2019, annual catch per fishing vessel (CPUE) was derived as an abundance index, and the gray catastrophe prediction GM(1,1) model was used to predict the future years of the Illex argentinus. The results showed that the upper years catastrophic year would occur in the years of 2021, 2028 and 2038 (CPUE ≥ 1615t per fishing vessel), and the lower catastrophe year would occur in the years of 2024, 2029 and 2036 (CPUE ≤ 784t per fishing vessel). Theoretically, the average relative error of the disaster model in rich years is 16.212%, the value of level deviation is 0.193, while the average relative error of the disaster model in poor years is 35.656%, and the value of level deviation is 0.199. The accuracy test for both models attain the level Ⅰ accuracy. According to the results, the grey catastrophe prediction model can simulate the years of abundance variation of Illex argentinus, and the prediction results can provide reference for the production and management of the species.