In this paper, with the help of measure of noncompactness together with Darbo-type fixed point theorem, we focus on the infinite system of third-order differential equations u′′′i + au ′′ i + bu ′ i + cui = fi(t,u1(t),u2(t), . . .) where fi ∈ C(R × R∞,R) is ω-periodic with respect to the first coordinate and a, b, c ∈ R are constants. The aim of this paper is to obtain the results with respect to the existence of ω-periodic solutions of the aforementioned system in the Banach sequence space `p (1 ≤ p < ∞) utilizing the respective Green’s function. Furthermore, some examples are provided to support our main results