Acute ischemic stroke (AIS) is the most common type of stroke in clinical practice, and individuals with stroke are more prone to psychological disorders than healthy individuals. This study aims to explore the incidence of anxiety and depression and related influencing factors in individuals with AIS. In brief, 680 individuals with AIS admitted to Chun'an County First People's Hospital from January 2021 to January 2023 were selected as the research subjects, and their clinical data were retrospectively analyzed. All patients were evaluated with the Self-Rating Anxiety Scale (SAS) and the Self-Rating Depression Scale (SDS) to observe the occurrence of anxiety and depression, and single-factor and multi-factor logistic regression were used to analyze the influencing factors of anxiety and depression. Among the 680 individuals with AIS, there were 63 cases of mild anxiety (9.26%), 25 cases of moderate anxiety (3.68%), and 8 cases of severe anxiety (1.18%), with a total of 96 cases (14.12%) with anxiety symptoms. Additionally, there were 74 cases of mild depression (10.88%), 28 cases of moderate depression (4.12%), and 10 cases of severe depression (1.47%), with a total of 112 cases with depression (16.47%). The results of univariate analysis showed that there was a weak correlation between age, body mass index, disease duration, marital status, and the development of anxiety and depression in individuals with AIS (p > 0.05). Educational level, underlying diseases, family income, and place of residence were found to influence the development of anxiety and depression in individuals with AIS (p < 0.05). The results of multivariate logistic regression analysis showed that educational level (no higher education), underlying diseases (with), family income (<50,000 yuan/year, the average exchange rate of RMB to USD was 6.7261), and place of residence (rural area) were influencing factors for the development of anxiety and depression in individuals with AIS (p < 0.05). Depression and anxiety are common psychological disorders in patients with AIS. The level of education (no higher education), underlying diseases (with), family income (<50,000 yuan/year), and place of residence (rural area) were risk factors that may lead to anxiety and depression in individuals with AIS. For those with risk factors for anxiety and depression, reasonable intervention should be continually provided to guide early disease prediction and treatment of anxiety and depression in individuals with AIS.