We study the Randall-Sundrum (RS) model that predict the existence of narrow resonances that appear in the di-lipton invariant mass distribution in proton-proton collisions. This gives final state with di-muon having large invariant mass from the decay of the RS1 graviton. A Large Hadron Collider (LHC) feasibility study for five-sigma discovery at 14 TeV was performed. The Kaluza-Klein graviton (GKK) production cross sections as a function of the graviton mass are presented and the limits on cross sections times branching ratio into muons to observe a 5 σ signal are presented. Our estimates based on integrated luminosity of 100 fb-1 and 1000 fb-1. The conclusion of our study is that the LHC can test the RS1 graviton existence if it is already existing with masses up to 2.6 TeV/c2 (3 TeV/c2) at luminosity of 100 fb-1 (1000 fb-1), when the parameter c (model parameter) is equal to 0.01. With the optimistic scenario, at c equal to 0.1, the GKK could be discovered if it is existing with mass up to 5 TeV/c2 with 100 fb-1 and mass up to 6.5 TeV/c2 with 1000 fb-1.