The invention provides a flexible peristaltic pump. The flexible peristaltic pump comprises a pump unit, a fixing unit and a connecting unit, wherein the pump unit is of a bag shaped structure manufactured through a driving film, comprising at least one opening channel through which liquid can flow in and out; a film prepared from an intelligent soft material can be externally excited to expand and contract under the eigenstrain so as to generate driving power for the peristaltic pump to pump in and pump out the liquid; the fixing unit is of a rigid structure and used for supporting the pump unit and the connecting unit, wherein the connecting unit is of a flexible structure for connecting the pump unit into a chain so as to ensure the flexibility characteristic of the whole peristaltic pump; an automatic valve is arranged in the connecting unit to control liquid to flow in and out; the fixing unit is used for supporting the pump unit. According to the flexible peristaltic pump, the driving film material and the special structure enable further simplifying of the peristaltic pump structure, so that the stability, reliability, efficiency and economy of the peristaltic pump can be improved, and the working noise can be reduced. The flexible peristaltic pump can be widely applied to the fields of chemical engineering, mining and metallurgy, paper-making, paint coatings, foods, ceramics, petroleum, water treatment, medicine preparation, and medical apparatuses and instruments in the future, and particularly plays an important role in artificial organ.