This article investigates the security consensus problem for fractional-order multiagent systems (FOMASs) with cyber attacks via the hybrid event-triggered and impulsive control strategy. First, based on the destructive characteristics of network attacks on communication channels, a method for separating partial network structures is proposed. Differing from other studies of multiagent systems, it considers here that the communication topological network consists of strong channel and weak channel networks, and its connectivity is not required. Then, to overcome bandwidth constraints, a new hybrid event-triggered and impulsive security consensus control approach is first designed, which only needs to detect the sampled data at instants of cyber attacks and impulse. Furthermore, applying the fractional Lyapunov stability analysis methods, several sufficient conditions are proposed to achieve the exponential consensus for FOMASs with cyber attacks. Meanwhile, some parameters in security consensus control protocol are acquired. Finally, from the perspective of numerical simulation visualization, the rationality and correctness of the proposed consensus security control method are verified.