Readmission is an important indicator of the quality of care. The purpose of this study was to explore the probabilities and predictors of 30-day and 1-year potentially preventable hospital readmission (PPR) after a patient’s first stroke. We used claims data from the National Health Insurance (NHI) from 2010 to 2018. Multinomial logistic regression was used to assess the predictors of 30-day and 1-year PPR. A total of 41,921 discharged stroke patients was identified. We found that hospital readmission rates were 15.48% within 30-days and 47.25% within 1-year. The PPR and non-PPR were 9.84% (4123) and 5.65% (2367) within 30-days, and 30.65% (12,849) and 16.60% (6959) within 1-year, respectively. The factors of older patients, type of stroke, shorter length of stay, higher Charlson Comorbidity Index (CCI), higher stroke severity index (SSI), regional hospital, public and private hospital, and hospital in the lower urbanized area were associated significantly with the 30-day PPR. In addition, the factors of male, hospitalization year, and monthly income were associated significantly with 1-year PPR. The ORs of long-term PPR showed a decreasing trend since implementing the national health insurance post-acute care (PAC) program in 2014 and a dramatic drop in 2018 after the government expanded the long-term care plan-LTC 2.0 in 2017. The results showed that better discharge planning, implementing post-acute care programs and long-term care plan-LTC 2.0 may benefit the care of stroke patients and help reduce long-term readmission in Taiwan.