The bivariate Exponentaited Weibull distribution is an important lifetime distribution in survival analysis. In this paper, Farlie-Gumbel-Morgenstern (FGM) copula and Exponentaited Weibull marginal distribution are used for creating bivariate distribution which is called FGM bivariate Exponentaited Weibull (FGMBEW) distribution. FGMBEW distribution is used for describing bivariate data that have weak correlation between variables in lifetime data. It is agood alternative to bivariate several lifetime distributions for modeling real-valued data in application. Some properties of the FGMBEW distribution are obtained such as product moment, moment generating function, reliability function and hazard function. Estimation method for parameters estimation is discussed for FGMBEW distribution namely maximum likelihood estimation. A simulations study is conducted to evaluate the performance of the estimators. Also, a real data set is introduced, analyzed to investigate the model and useful results are obtained for illustrative purposes.