We study the folding mechanism of an analog of the C-peptide of ribonuclease A in explicit water by a replica-exchange multicanonical molecular dynamics simulation based on all-atom models. The multicanonical weight factor was determined by the combined use of the multicanonical replica-exchange method and the replica-exchange multicanonical algorithm. Using statistically reliable data thus obtained, we have examined the free-energy landscape of the peptide system. The global-minimum free-energy state in the landscape at room temperature has an alpha-helix structure with a distortion near the N-terminus. The state also has a salt bridge between Glu(-)-2 and Arg(+)-10 and an aromatic-aromatic interaction between Phe-8 and His(+)-12, both of which have been observed in x-ray and other experimental measurements. Principal component analysis clearly shows the different roles of these side-chain interactions in the peptide folding. The side-chain interaction between Phe-8 and His(+)-12 greatly enhances the stability of helical structure toward the C-terminal end, whereas the salt bridge between Glu(-)-2 and Arg(+)-10 mainly works as a restraint to prevent the alpha-helix structure from extending to the N-terminus. The free-energy landscape of C-peptide reveals a funnel-like shape where all of these interactions consistently exist only in the global-minimum state. This is the major reason why the native structure of the short helical peptide shows significant stability at low temperatures.