Compound distributions gained their importance from the fact that natural factors have compound effects, as in the medical, social and logical experiments. Dubey (1968) introduced the compound Weibull by compounding Weibull distribution with gamma distribution. The main aim of this paper is to define a bivariate generalized Burr (compound Weibull) distribution so that the marginals have univariate generalized Burr distributions. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance- covariance matrix have been obtained. Some simulations have been performed to see the performances of the MLEs. One data analysis has been performed for illustrative purpose.