Climate change influences all living beings. Wheat aphids deplete the nutritional value of wheat and affect the production of wheat in changing climate. In this study, we attempt to explain the ecological mechanisms of how climate change affects wheat aphids by simulating the relationship between climate and the abundance of wheat aphids, which will not only aid in improving wheat aphid forecasting and the effectiveness of prevention and treatment, but also help mitigate food crises. Fuzzy cognitive maps (FCM) are an effective tool for portraying complex systems. Using Sitobion avenae and climatological data collected in China, we made use of differential evolution (DE) algorithms to construct FCM models that directly illustrate the effect of climate on wheat aphid abundance. The relationships among climate and wheat aphids at different growth stages (I-III instar larvae, IV instar larvae with wings, IV instar larvae without wings, adult with wings, adult without wings) were established. The analysis results from the FCM models show that temperature positively influences wheat aphids most. Moreover, these models can be used to determine the numerical value of each climate factor and the abundance of wheat aphids quantitatively. Furthermore, the two overall relationship models between climate and wheat aphids were constructed and the experimental results show that natural enemies and highest daily temperature affect wheat aphids most. Natural enemies and highest daily temperature exert negative and positive impacts on wheat aphids respectively. Some interrelationships among wheat aphids at all growth stages and the internal relationships among climate factors were also shown.