Burr Type III distribution have been mainly used in statistical modeling of events in a variety of applied mathematical contexts such as fracture roughness, life testing, meteorology, modeling crop prices, forestry, reliability analysis. Our aim of this work is to construct a bivariate Burr Type III distribution and some of its structural properties such as bivariate probability density function and it^'s marginal, joint cumulative distribution and it^'s marginal, reliability and hazard rate function are studied. The maximum likelihood estimators of the parameters are derived. The Bayes estimators of the parameters based on the squared error loss function and Bayesian prediction of the future observations are presented. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, one data set under the proposed distributions to illustrate their flexibility for real-life applications is analyzed.