Abstract: Firstly，birandom theory is introduced.Secondly some concepts such as birandom empirical risk functional，birandom expected risk functional and birandom empirical risk minimization principle are proposed.Finally the key theorem of statistical learning theory based on birandom samples is proved，and the bounds on the rate of uniform convergence of learning process are discussed.The investigations will help lay essential theoretical foundations for the systematic and comprehensive development of statistical learning theory and support vector machine based on uncertain samples.