Hospital efficiency & Productivity analysis, is an important issue in the health economics. Furthermore, the study analyze the efficiency and productivity in the hospitals, from two viewpoints: firstly, Data Envelopment Analysis (DEA) used to measure the relative efficiency of the hospitals with applying (CCR) approach. Secondly, Luenberger Productivity Indicator (LPI) used to measure the change (progress) in productivity of consecutive time periods. The study model has been tested and implemented on four case studies based on changing in inputs and outputs variables, of three hospitals in the study district (Baghdad) to analyze their efficiency, in two years period (2014-2015), with three inputs variables and five outputs variables. The results of using DEA technique shows that Al- Alwaiya Children's hospital only still efficient in four cases, while, other hospitals (Ibn Al- Balady & Fatima Al-Zahraa) change their efficiency by changing the case, then by using LPI technique, the results indicate that the (Ibn Al- Balady) hospital has productivity growth in three cases. The Fatima Al-Zahraa hospital has productivity decline in two cases and has growth in one case only. Finally the Al- Alwaiya Children's hospital has productivity growth in all cases during period (2014 – 2015).