In the present study, we investigate different types of 1D peanut-shaped fullerene polymers (PSFPs) using density functional theory to understand the electronic states and the energetic stability of curved carbon nanomaterials. We generated 53 different models of the 1D PSFPs by means of the generalized Stone-Wales transformations and performed structural optimization for each model. Band structures of the 1D PSFPs exhibit either metallic or semiconducting property according to the geometrical structures. We find that the energetic stability of the 1D PSFPs depends on the geometry: the more octagon and pentagon-octagon pairs (heptagons and hexagon-heptagon pairs) in their geometrical structures, the more stable (unstable) the 1D PSFPs.