The periodic solutions for a class of Volterra differential systems with delays are discussed. By using techniques such as the fundamental solution matrix and Floquet theory, the Volterra system is integrally transformed to construct a new expression for the system solution; By using the Krasnoselskii fixed point method, the existence of periodic solutions for the studied system is obtained; the sufficient conditions for the uniqueness of the periodic solution of the system are obtained by using the contraction mapping principle. Finally, an example is given to verify the effectiveness of the conclusion.