‎In the recent years‎, ‎bivariate lifetime data 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 reported some simulation results and performed one data analysis for illustrative purposes‎.