New monetary literatures widely concentrates on the importance of institutional arrangements in the effectiveness of monetary policy. The debate regarding the optimal institutional design of central banks, independence and conservatism are usually considered to be the most important ingredients for a stable and successful monetary policy. Therefore, the purpose of this study is to deal with the institutional arrangements of monetary policy especially central bank Independence (CBI) and central bank Conservatism (CBC). Indices used by Grilli et al. (1991), Cukierman (1992), Mathew (2006) and Dumiter (2009) were applied to calculate the CBI during 1961-2016, and CBC in Iran using a dynamic optimal solution under commitment in Barro-Gordon and New-Keynesian forward looking Philips Curve models. Results show that the relative concern on inflation is smaller than that on output gap for the central bank of Iran. Also results regarding the calculations of CBI based on different indices reveals the fact of insufficient independence of central bank in Iran.