Exponentiated Exponential (EE) distribution is the development of Exponential Distribution by adding α as a shape parameter. This distribution can solve unflexibility issue in Exponential distribution. In order to make inferences about any cases modeled with EE distribution, parameter estimation is required. This paper will discuss about parameter estimation of Exponentiated Exponential distribution for left censored data using Bayesian method. Parameter estimation procedure are selection of prior distribution which is conjugate prior, likelihood construction for left censored data, and then forming posterior distribution. Bayes estimator can be obtained by minimize posterior risk based on Squared Error Loss Function (SELF) and Precautionary Loss Function (PLF). After Bayes estimator is obtained, simulation is done to compare the results of Bayes estimator using SELF and PLF which are seen from the result of Mean Square Error (MSE). Loss function is said to be more effective to obtain Bayes estimator if the resulting Bayes estimator yield smaller MSE. Based on simulation, PLF more effective for α ≤ 1, while SELF more effective for α > 1.