Recently, Cyber-Physical-Social Systems (CPSS) have been introduced as a new information physics system, which enables personnel organizations to control physical entities in a reliable, real-time, secure, and collaborative manner through cyberspace. Moreover, with the maturity of edge computing technology, the data generated by physical entities in CPSS are usually sent to edge computing nodes for effective processing. Nevertheless, it remains a challenge to ensure that edge nodes maintain load balance while minimizing the completion time in the event of the edge node outage. Given these problems, a Unique Task Offloading Method (UTOM) for CPSS is designed in this paper. Technically, the system model is constructed firstly and then a multi-objective problem is defined. Afterward, Improving the Strength Pareto Evolutionary Algorithm (SPEA2) is utilized to generate the feasible solutions of the above problem, whose aims are optimizing the propagation time and achieving load balance. Furthermore, the normalization method has been leveraged to produce standard data and select the global optimal solution. Finally, several necessary experiments of UTOM are introduced in detail.