This paper develops and estimates a Dynamic Stochastic General Equilibrium (DSGE) model for the Azerbaijan economy. The model incorporates with open economy features such as habit formation and cost of adjustment in capital accumlation. The model has five types of economic agents: households, firms, aggregators, the rest of the world and the government. It includes a number of shocks and frictions. The model is estimated with Bayesian techniques using thirteen macro economic variables: GDP inflation, private consumption good inflation, investment good inflation, real wages, real private consumption, real investment, real GDP, employment, real exports, real imports, nominal interest rate, foreign real GDP and foreign nominal interest rate. The main aim of the paper is to estimate various specifications of a small open economy model in order to determine the model which provides a better fit of Azerbaijan economy.