As an emerging network paradigm, Space-Air-Ground integrated networks (SAGIN) has attracted the attentions from academia and industry. That is because SAGIN can implement seamless global coverage and connections among electronic devices in space, air, and ground spaces. Additionally, the shortages of computing and storage resources in mobile devices greatly affect the quality of experiences for intelligent applications. Hence, we devise to integrate SAGIN as an abundant resource pool into mobile edge computing environments (MEC). To facilitate efficient processing, we need to solve the optimal task offloading decisions. Different from the existing MEC task offloading solutions, we have to face some new challenges, such as the fluctuation of processing capability for an edge computing node, the uncertainty of the transmission latency caused by the heterogeneous network protocols, the uncertain amount of uploaded tasks during a period, and so on. In this paper, we firstly describe a task offloading decision problem in new challenge environments. But, we cannot use the standard robust optimization and stochastic optimization methods to obtain the optimal result under the uncertain network environments. In this paper, we propose the condition value at risk-aware distributionally robust optimization algorithm, named as CVAR-DRO, to solve the task offloading decision problem. The proposed CVAR-DRO method combines the distributionally robust optimization and the condition value at risk model for solving the optimal result. And then, We have evaluated our approach in simulation SAGIN environments with the confidence interval, the number of mobile task-offloading and the various parameters. We compare our proposed CVAR-DRO algorithm with the state-of-the-art algorithms, such as the standard robust optimization algorithm, the stochastic optimization algorithm, the DRO algorithm, and the brute algorithm. The experimental results show that CVAR-DRO can get a sub-optimal mobile task-offloading decision. Overall, CVAR-DRO is more robust than others to the new challenges mentioned above in SAGIN.