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Background Korea’s rapidly aging population has led to a rise in the prevalence of knee osteoarthritis (which reached upwards of 21.3% in 2017) in elderly people aged 65 years and over. Most patients with knee osteoarthritis require ongoing management in the community or through primary care. Continuity of care is a desirable attribute of primary care. However, previous studies on the association between continuity of care and health outcomes have focused on specific disease populations, particularly diabetes mellitus and hypertension. The objectives of this study were to determine whether there is an association between continuity of care for outpatients with knee osteoarthritis and health outcomes. Methods We conducted a cohort study using claims data from 2014. The study population included 131,566 patients. We measured hospital admission and medical costs during the final 3 months and the continuity of care by Most Frequent Provider Continuity (MFPC), Modified Modified Continuity Index (MMCI), and Continuity of Care (COC) index in the 9 preceding months, using multiple logistic regression analyses to determine which index best explains continuity. We evaluated the relationship between COC and hospital admissions, using negative binomial regression analysis due to over-dispersion. Finally, multiple regressions were used to examine the relationship between the COC and medical costs. Results We selected the COC index to determine the association between hospital admission and cost; the area under the receiver operating characteristic curve (AUC) of the COC was the largest (0.904), while those for the MFPC (0.894) and MMCI (0.893) were similar. The negative binomial regression analysis showed that continuity of care was significantly related to hospitalization, with the relative risk (RR) of hospital admission being low for patients with high continuity of care [RR = 27.17 for those with the reference group COC (0.76–1.00); 95% CI, 3.09–3.51]. Continuity of care was significantly related to medical costs after considering other covariates. A higher COC index was associated with a lower cost. Conclusions Higher continuity of care for knee osteoarthritis patients might decrease hospital admission and medical costs. Electronic supplementary material The online version of this article (10.1186/s12913-018-2951-y) contains supplementary material, which is available to authorized users.