The purpose of the present paper is to study the existence and attractivity of $S$-asymptotic $\omega$-periodic mild solution to semilinear integro-differential systems with nonlocal conditions via resolvent operators in the sense given by Grimmer. The existence, as well as the uniqueness results are established by means of Perov and Schaefer fixed point theorems combined with a vector approach that uses matrices that converge to zero which was given in generalized Banach space. The obtained result is illustrated by an example at the end.