In recent years, bivariate lifetime distributions are often used to model reliability and survival data. In this paper, we introduce a bivariate Burr III distribution, so that the marginals have Burr III  distributions. It is observed that the joint probability density function, the joint cumulative distribution function and the joint survival distribution function can be expressed in compact forms.  We suggest to use the ECM algorithm to compute the maximum likelihood estimators of the unknown parameters. We report some simulation results and perform one data analysis for illustrative purposes.