Gel foam has the advantages of gel and foam and shows good prospects for applications in the fields of fire prevention and extinguishing. Rheology has a significant impact on the application of gel foam, but there is little related research. In the present study, hydrophilic silica nanoparticles (NPs) and water-soluble polymer xanthan gum (XG) were combined with fluorocarbon surfactant (FS-50) and hydrocarbon surfactant (APG0810) to create gel foam. The foaming ability and foam drainage were evaluated. The gel foam’s rheology, including its flow behavior and viscoelasticity, was systematically investigated. The results show that the foaming of the FS-50/APG0810 mixture decreases but the foam drainage increases in the presence of NPs and/or XG. All of the foams belong to the category of non-Newtonian fluids with shear thinning behavior. The flow curves of the foams are consistent with the Cross model. The presence of XG/NPs enhanced the foam viscoelasticity of the FS-50/APG0810 mixture. The silica NPs showed a better ability to enhance foam viscoelasticity but a worse ability to stabilize the foam compared to XG. This research can offer theoretical support for the industrial usage of gel foam.