This study estimates the efficiency of 19 tertiary hospitals in Taiwan using a two-stage analysis of Data Envelopment Analysis (DEA) and TOBIT regression. It is a retrospective panel-data study and includes all the tertiary hospitals in Taiwan. The data were sourced from open information hospitals legally required to disclose to the National Health Insurance (NHI) Administration, Ministry of Health and Welfare. The variables, including five inputs (total hospital beds, total physicians, gross equipment, fixed assets net value, the rate of emergency transfer in-patient stay over 48 h) and six outputs (surplus or deficit of appropriation, length of stay, the total relative value units [RVUs] for outpatient services, total RVUs for inpatient services, self-pay income, modified EBITDA) were adopted into the Charnes, Cooper and Rhodes (CCR) and Banker, Charnes and Cooper (BCC) model. In the CCR model, the technical efficiency (TE) from 2015–2018 increases annually, and the average efficiency of all tertiary hospitals is 96.0%. In the BCC model, the highest pure technical efficiency (PTE) was in 2018 and the average efficiency of all medical centers is 99.1%. The average scale efficiency of all medical centers was 96.8% in the BBC model, meaning investment can be reduced by 3.2% and the current production level can be maintained with a fixed return to scale. Correlation coefficient analysis shows that all variables are correlated positively; the highest was the number of beds and the number of days in hospital (r = 0.988). The results show that TE in the CCR model was similar to PTE in the BCC model in four years. The difference analysis shows that more hospitals must improve regarding surplus or deficit of appropriation, modified EBITDA, and self-pay income. TOBIT regression reveals that the higher the bed-occupancy rate and turnover rate of fixed assets, the higher the TE; and the higher number of hospital beds per 100,000 people and turnover rate of fixed assets, the higher the PTE. DEA and TOBIT regression are used to analyze the other factors that affect medical center efficiency, and different categories of hospitals are chosen to assess whether different years or different types of medical centers affect operational performance. This study provides reference values for the improvable directions of relevant large hospitals’ inefficiency decision-making units through reference group analysis and slack variable analysis.