<p>This work is devoted to the study of positive solutions and propagation phenomena of time-space periodic Lotka-Volterra competition system. Firstly, we prove the existence of positive periodic solutions by using the method of sub- and supersolutions. Then, we prove the uniqueness as well as the global stability of the positive periodic solution by establishing the bounds of positive periodic solutions and developing an iterative method. Finally, by using the abstract theory of time-space periodic monotone semiflows, we establish some propagation phenomena between the positive periodic solution and a semitrivial one. Our arguments in proving the uniqueness result seem to be the first that may also be used to study entire solutions of periodic parabolic boundary-value problems.</p>