Background Potentially, the risk of morbidity and mortality during pregnancy and child birth can be prevented through comprehensive, quality antenatal care services. The high maternal mortality rate in developing countries, including Ethiopia, is related to poor quality of antenatal care services and is still a major public health problem. The aim of this study is to assess the quality of antenatal care and associated factors in public health centers in Addis Ababa, Ethiopia. Methods An institution-based cross-sectional study was conducted using a quantitative method from December 10 to January 30, 2020. A total of 616 study participants were selected by a systematic random sampling technique. Data was collected using pre-tested structured interview administered questionnaires. The data was entered into Epi-info version 7.2.1 and analyzed by SPSS version 24. Bivariate and multivariable logistic regressions were performed to identify the presence and strength of the association between the outcome and predictor variables. Results Overall, 33% of pregnant women received good-quality antenatal care. Satisfaction with antenatal care service, antenatal care initiation time, maintaining confidentiality, and waiting time become significant predictors of the quality of antenatal care. As a result, a lack of confidential care (AOR = 0.37; 95% CI, (0.40, 0.88)), a long waiting time (AOR = 0.6, 95% CI, (0.48, 0.88)), and no satisfaction with ANC services (AOR = 0.26; 95% CI, (0.109, 0.36)) were identified as factors impeding the quality of antenatal care. While starting ANC later than four months of pregnancy was found to be a positive predictor of the quality of antenatal care (AOR = 1.9, 95% CI: (1.21, 3.12)). Conclusion Only one-third of pregnant mothers received good quality antenatal care. Lack of confidential care, long waiting time and no satisfaction with antenatal care services were factors hindering the quality of antenatal care. While initiation of antenatal care after four months of pregnancy was a positive predictor of the quality of antenatal care.