(1) Background: Stroke is an important topic in the healthcare industry. The objective of the present study was to investigate patients’ sociodemographic characteristics, health status, continuity of care, self-management, and other predictors that affect their self-management. (2) Methods: This cross-sectional correlational study was carried out from March to September 2020, and included a total of 150 patients aged 20 and above who were diagnosed within the past 6 months. The research participants were selected from the Division of Neurology, Department of Internal Medicine/Department of Surgery, at a medical center in Central Taiwan. (3) Results: The mean self-management score of patients with stroke was 110.50 points (30–150 points). As shown in the stepwise regression analysis, the overall regression model explained approximately 44.5% of the variance in self-management. Educational level (10.8%), frequency of exercise per week (2.1%), time that patients were affected by stroke (2.4%), and continuity of care (29.2%) were the main predictors affecting the self-management of stroke patients. (4) Conclusions: To improve stroke patients’ self-management, medical teams should provide appropriate continuity of care to those with lower educational levels, those without exercise habits, and those who experienced a stroke within the past six months.