The infrared absorption spectra of acetone and methanol mixtures have been investigated in a solid argon matrix at 9 K. A number of intramolecular complex bands were observed both in the acetone and methanol fundamental regions. From the concentration dependence of the infrared spectral pattern, acetone and methanol seemed to form a 1:1 binary complex. Noticeable red-shifts of the C=O stretching mode of acetone as well as the O-H stretching mode of methanol suggest that the two molecules are bound mainly through a H-bond between the carbonyl oxygen and the hydroxyl hydrogen atoms. A relatively weaker H-bonded interaction appeared also to act between the oxygen atom of methanol and a hydrogen atom of acetone. This view was found to be consistent with ab initio SCF, MP2, and DFT level computations. The most stable structure calculated was found to possess those two kinds of H-bonds, assuming a planar six-membered ring-like structure.