The nature of fluorescence (FL) quenching for the aqueous solutions of adenosine triphosphate (ATP) with calix[4]arenes C-107 in the presence of silver nitrate AgNO3 is studied. It is shown that, for the water solutions of ATP and calix[4]arenes C-107 at a constant concentration of ATP molecules with an increase in the content of C-107, a complex nature of the PL quenching is observed, while maintaining the position of the PL band near 395 nm (λex = 285 nm). Its complexity is based, on the one hand, in the wide range of concentrations of C-107, at which it occurs, and, on the other hand, there are gaps in the quenching values for individual concentrations of calix[4]arene, near which it changes slightly. The indicated nature of the PL quenching significantly depends on the wavelength of excitation and the temperature. Similar quenching behavior is preserved, when AgNO3s alts are added to the ATP–C-107 mixtures, (CATP = CC-107 = 1 × 10−4M) in the concentration range from 1 × 10−4M to 1 × 10−3M. The computer modeling shows that the system ATP–C-107 can form energetically stable complexes, when ATP is located on the top of the calix[4]arene and along the wall of it due to π-π-stacking interaction, and the complexes are characterized by a shrinking of the energy bands.