Summary: We revisit the famous periodic Lotka-Volterra competitive system. Some new and interesting sufficient conditions are obtained to guarantee the existence and global asymptotic stability of periodic solutions in the Lotka-Volterra competitive system. Our method is based on Mawhin’s coincidence degree, matrix’s spectral theory, and some new estimation techniques for the priori bounds of unknown solutions to the equation \(Lx=\lambda Nx\). Due to this new method, our new results are much different from the known results in the previous literature. Finally, some examples and their simulations show the feasibility of our results.