Background: Familial hypercholesterolemia (FH) is an inherited disorder characterized by significantly elevated levels of low-density lipoprotein (LDL) cholesterol and is usually diagnosed after the occurrence of major adverse cardiovascular event. Aim: The aim of this study was to evaluate FH existence, increase awareness of this disorder, and highlight the importance of early treatment which leads to a reduction of premature cardiovascular events and death. Methods: The research had a cross-sectional, descriptive, and analytical character, and included 6881 (n = 6881) patients who were hospitalized in the Clinic for Heart, Blood Vessel and Rheumatic Diseases, Clinical Center University of Sarajevo, Sarajevo, Bosnia and Herzegovina, in the period from January 2019 to January 2021. LDL values were analyzed, and all patients with LDL ≥4 mmol/L were included in the study. The Dutch Lipid Score was calculated for all patients, and the findings of invasive coronary angiography were taken into account in those patients for whom it was performed. Results: From 6881 patients, 74 patients had LDL ≥4 mmol/L. Possible FH (score: 3–5) was found in 25 patients, probable FH (score: 6–8) in 2 patients, while the diagnosis of definite FH was not made in any patient. A ST-elevation myocardial infarction was an indication for hospitalization in 44.60% (n = 33), hypertension in 14.87% (n = 11), and angina pectoris in 14.87% (n = 11) of patients. Patients under the age of 65 had higher Dutch Lipid Score compared to the patients above the age of 65, regardless of male or female. Correlational analysis indicated a significant positive relationship between Dutch Lipid Score and level of cholesterol (r =0.385; P < 0.01) and LDL (r = 0.401; P < 0.001). Statistically significant predictors in the explanation of FH were age (β = −0.45; P < 0.001) and LDL (β = 0.52; P < 0.001). Conclusion: LDL values and age are the main determinants of the FH existence, and the effect on LDL values should be imperative in clinical practice.