This paper introduces a new consensus protocol in a multi-agent system (MAS) with complementary links and a time delay. According to this protocol, agents in an MAS receive information from some agents immediately, and from the others with a delay. This protocol is a special case of a more general model, commonly applied to analyze traffic flows, forecast price dynamics in commodity markets, and describe biological and epidemiological processes. A stability condition is derived under which the protocol converges regardless of the delay. Tsypkin’s test is used to obtain the boundary delay, which depends on the spectrum of the Laplacian matrix. The frameworks of algebraic graph theory, control theory, and operational calculus are employed to establish the asymptotic behavior of a stable MAS for different initial conditions and, consequently, a condition for reaching consensus for any initial value vector. As demonstrated, if the influence digraph is balanced, the time-delay consensus protocol will converge to an average consensus.