This article addresses the quasi-sure consensus problem for multiagent systems (MASs) in the context of denial-of-service (DoS) attacks. Instead of adopting the conventional noise-based protocols driven by Brownian motion, a novel G-noise communication protocol is first proposed to realize the consensus. Moreover, the consensus protocol not only contains time-varying and nonlinear characteristics but also focuses on DoS attacks. The protocol driven by the G-Brownian motion is characterized in the sublinear expectation framework, which leads to the infeasibility of the existing theory. To overcome the difficulty, a new theoretical framework is established to develop a consensus criterion. More specifically, first, the nonzero property of MASs is introduced to ensure the rationality of the construction for the Lyapunov function. Then, a sufficient criterion for guaranteeing the consensus of MASs is demonstrated by utilizing the Lyapunov method, graph theory, and stochastic analysis theory, which depends on DoS duration, noise intensity, and G-Brownian motion parameters. Ultimately, theoretical results are associated with islanded microgrid systems with numerical simulation being exploited.