Geometries and electronic structures of methyl azide and its dimers have been calculated firstly by using ab initio method at the HF level with the 6-311G^** basis set. The intermolecular interaction energy is calculated with MP2 electron correlation correction, basis set superposition error (BSSE) correction and zero point energy (ZPE) correction. The most stable dimer (the binding energy of 9.49 kJ·mol^-1) possesses a six-membered ring with two C-H...N hydrogen bonds and belongs to D_2h group. The effect of methyl internal rotation on the interaction energy is investigated. Natural bond orbital (NBO) analysis is performed to reveal the origin of the interaction. The harmonic vibrational analysis is used to study the optimized structure of the monomer and six dimers, and IR spectrum shifts are discussed. Based on the statistical thermodynamic method, the changes of thermodynamic properties from the monomer to dimer with the temperature ranging from 273.15 K to 800.00 K have been obtained.