In this work, we report a study on the infrared transmission spectroscopy of the double perovskite Ba2YMoO6. At 300？K, three bands are observed at ～255.1？cm^？1, ～343.4？cm^？1, and ～561.5？cm^？1, which are related to the motion between the cation Ba2+ and the anion YMO6？2, the Y-O stretching motion, and the stretching vibration of the MoO6 octahedron, respectively. These modes continue to harden upon cooling owing to the shrink of the lattice constant. When the temperature decreases to T ≤ 130？K around which the spin singlet dimer begins to form, an additional phonon mode appears at ～611？cm^？1, suggesting the occurrence of local distortion of MoO6 octahedra. With further decrease of the temperature, its intensity enhances and its peak position keeps unchanged. These results indicate that the formation of the spin singlet dimers is accompanied with the occurrence of the local structure distortion of MoO6 octahedra, providing evidence for the strong spin-phonon coupling in the double perovskite Ba2YMoO6.