Systematic search of the potential energy surface of tetrapeptide glycine-phenylalanine-glycine-glycine (GFGG) in gas phase is conducted by a combination of PM3, HF and BHandHLYP methods. The conformational search method is described in detail. The relative electronic energies, zero point vibrational energies, dipole moments, rotational constants, vertical ionization energies and the temperature dependent conformational distributions for a number of important conformers are obtained. The structural characteristics of these conformers are analyzed and it is found that the entropic effect is a dominating factor in determining the relative stabilities of the conformers. The measurements of dipole moments and some characteristic IR mode are shown to be effective approaches to verify the theoretical prediction. The structures of the low energy GFGG conformers are also analyzed in their connection with the secondary structures of proteins. Similarity between the local structures of low energy GFGG conformers and the α-helix is discussed and many β- and γ-turn local structures in GFGG conformers are found.