As one of the most promising networks, the space–air–ground–aqua integrated network (SAGAIN) has the characteristics of wide coverage and large information capacity, which can meet various requests from users in different domains. With the rapid growth of data and information generated by the Internet of Things (IoT), SAGAIN has received much attention in recent years. However, the existing network architectures are not capable of providing personalized network services according to different task types in SAGAIN. Besides, they cannot deal with many problems in SAGAIN well, such as heterogeneous network disconnection, high network delay, intermittent interruption, and unbalanced network load. In this article, in order to solve the abovementioned problems, we propose a novel architecture for SAGAIN named task-oriented intelligent networking architecture (TOINA). First, we apply the edge-cloud computing technology and network domain division in TOINA to realize intelligent networking and reduce the latency. Second, the task-oriented networking method is proposed to provide personalized network services and increase network intelligence. Third, we intend to leverage the information center network (ICN) paradigm to build the SAGAIN and optimize the content naming rules. Furthermore, a preprocessing layer was added in the network protocol stack to perform the heterogeneous network convergence in SAGAIN. In addition, some security technologies related to network architecture are considered in SAGAIN. This article presents the background, rationale, and benefits of the TOINA for SAGAIN. Besides, a specific case is studied to illustrate the network architecture work process further.