Intermolecular interaction energies of five C2H4-CH4 dimers and two C2H6-CH4 dimers were calculated. Dunning's correlation consistent basis sets (cc-pVXZ, X = D, T, Q, and 5) were used to estimate the MP2 interaction energies of the dimers at the basis set limit. The dimer in which the C-H bond of CH4 points to the C=C bond of C2H4 has slightly larger bonding energy than the other four C2H4-CH4 dimers. The estimated CCSD(T) interaction energy of this dimer at the basis set limit is -0.49 kcal/mol, which is about 10% of the bonding energy of water dimer. The large correlation interaction energy (-0.86 kcal/mol), calculated as the difference between the HF and post-SCF interaction energies, suggests that the dispersion interaction is significantly important for the attraction between C2H4 and CH4. The analysis of the electrostatic interaction using distributed multipoles shows that the attractive electrostatic interaction (-0.24 kcal/mol) is playing important role to stabilize this dimer. On the other hand, the electrostatic interaction is negligible for the C2H6-CH4 dimers. The C-H bond of CH4 does not prefer to point to the C-C bond of C2H6.