We studied an elastic proton--proton scattering process at large center-of-mass energy and small momentum transfer, i.e. the Regge limit, using a holographic QCD model. We computed the total amplitude for a vector meson and a glueball exchange from tree-level Feynman diagrams. We analyzed an open-string scattering amplitude and a closed-string scattering amplitude to include higher-spin states to the mesonic (Reggeon) and glueball (Pomeron) trajectories. The Reggeized amplitude was used to calculate the differential cross-section of the process.