Background: Patients with angina are often suffering from comorbidities such as varying degrees of hepatic dysfunction. However, the impact of angina on the incidence of hepatic failure (HF) remains unclear. Methods: The genetic data were retrieved from genome-wide association studies. Five Mendelian randomization methods were used to investigate the causal relationship between unstable angina (UA), stable angina (SA), and HF. The result of the Inverse variance weighted (IVW) method was deemed the principal result. In addition, we performed a comprehensive sensitivity analysis to verify the robustness of the results. Results: The IVW results showed that UA (Odds ratio (OR): 2.055, 95% confidence interval (CI): 1.171–3.606, p = 0.012) was causally associated with the incidence of HF. SA (OR: 1.122, 95% CI: 0.738–1.706, p = 0.591) was not causally associated with the incidence of HF. Sensitivity analysis did not identify any bias in the results. Conclusions: UA turned out to be a risk factor for HF. SA does not have a significant causal effect on HF. Therefore, it is highly recommended that patients with chronic liver disease seek prompt medical attention and undergo regular monitoring of liver function when experiencing UA. This may help them to reduce the risk of HF.