The bivariate generalized Rayleigh distribution is an important lifetime distribution in survival analysis. In this paper, Clayton copula and generalized Rayleigh marginal distribution are used for creating bivariate distribution which are called bivariate generalized Rayleigh based on Clayton copula (Clayton-BGR) distribution. The reliability function and hazard function were obtained for bivariate generalized Rayleigh distribution. Two different estimation methods for the unknown parameters of the Clayton-BGR model were discussed.To evaluate the performance of the estimators, a Monte Carlo simulation study was conducted to compare the efficiency between the Clayton-BGR and anther models. Also, a real data set is analyzed to investigate the models and useful results are obtained for illustrative purposes.