We theoretically investigate the transport property of graphene surface plasmon polaritons (GSPPs) on curved graphene substrates. The dispersion relationship, propagation length, and field confinement are calculated by an analytical method and compared with those on planar substrates. Based on our theory, the bend of graphene nearly does not affect the property of GSPPs except for an extremely small shift to the lower frequency for the same effective mode index. The field distributions and the eigenfrequencies of GSPPs on planar and cylindrical substrates are calculated by the finite element method, which validates our theoretical analysis. Moreover, three types of graphene-guided optical interconnections of GSPPs, namely, planar to curved graphene film, curved to planar graphene film, and curved to curved graphene film, are proposed and examined in detail. The theoretical results show that the GSPPs propagation on curved graphene substrates and interconnections will not induce any additional losses if the phase-matching condition is satisfied. Additionally, the extreme tiny size of curved graphene for interconnection at a certain spectra range is predicted by our theory and validated by the simulation of 90° turning of GSPPs. The bending effect on the property of GSPPs is systematically analyzed and identified. Our studies would be helpful to instruct design of plasmonic devices involving curved GSPPs, such as nanophotonic circuits, flexible plasmonic, and biocompatible devices.