The effect of graphene content, spinning flow rate, and distance on the chemical and thermal stability of electrospinned polyvinylidene fluoride (PVDF)/graphene composite membranes was systematically investigated. Long-duration soaking experiments by three typical solution media, diluted hydrochloric acid, dimethyl sulfoxide, and mixed-solution of lithium hexafluorophosphate/methyl ethyl carbonate, were used to evaluate the chemical stability of the selected samples. The relevant results of relative mass change rate all indicate that the chemical stability of PVDF composite materials increases with increasing graphene content as well as flow rate or decreasing distance. Moreover, there is a clear consistency between thermal stability and chemical stability. The results of the thermal shrinkage rate evidence that the thermal stability of the samples could be enhanced by increasing graphene content, flow rate, and decreasing spinning distance.