We investigated the binding nature of the 1,2,3-alternate calix[6]arene with one piperidine, two piperidines, and two triethyl amines with a special emphasis on the hydrogen bonding networks by density functional theory calculations. The 1,2,3-alternate calix[6]arene strongly binds with piperidines and triethylamines at two different binding sites, exo and endo sites. In the two binding sites, the hydrogen bonding nature shows a characteristic difference. In the exo site, there formed only one hydrogen bond, while in the endo site, two hydrogen bonds except for the triethylamine. The proton transfer within the hydrogen bonding and the hydrogen bonding types, normal hydrogen bonding (NHB), short strong hydrogen bond (SSHB), and low barrier hydrogen bonding (LBHB), will be discussed in detail.