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Casualties during crowd evacuation in many unexpected events are closely related to panic behaviors. In this paper the evacuation crowd system is abstracted into a dynamic complex network composed of three types of people, namely calm people, panic people, and herding people, as well as their interactions. The mathematical model of these interactions is established based on complex network theory. Further, the evolution of herding people to panic people is interpreted by a specific concept of ''herding-panic threshold,'' as well as its utility threshold model, in which the own characteristics of herding people and the external pressure from the surrounding crowd are comprehensively considered. To verify the rationality of some assumption in the utility threshold model, a questionnaire survey about the evacuation psychological behaviors is carried out. Through theoretical analysis and simulation, the influence of some key parameters on the herding-panic behavior is discussed in detail, via analyzing the change of panic rate. Some safety measures to control herding-panic in evacuation are also suggested.