Adsorption behavior of counterions under a Langmuir monolayer was investigated by sum-frequency generation (SFG) spectroscopy. By comparing SFG spectra of arachidic acid (AA) Langmuir monolayer/water interface with and without added salt, it was found that the simple trivalent cation $La^{3+}$ adsorbed on AA monolayer only when the carboxylic headgroups are charged (deprotonated), implying that counterion adsorption is induced by Coulomb interaction. On the other hand, metal hydroxide complex $Fe(OH)_3$ adsorbed even on a charge-neutral AA monolayer, indicating that the adsorption of iron hydroxide is due to chemical interaction such as covalent or hydrogen bonding to the headgroup of the molecules at the monolayer.