The effect of vibrational relaxation on the photodesorption dynamics of NO from a Pt(111) surface has been investigated theoretically. Although this system has been studied in many previous works, the relaxation of NO stretching vibration due to the interaction with electron-hole pairs in metals has not been included in conventional models. Although the relaxation lifetimes of the first-excited vibrational state of diatomic molecules adsorbed on metal surfaces are generally in the range 0.1-1 ps, the desorption dynamics of NO is complete in about 1 ps. Therefore, it is considered that the vibrational relaxation can influence the vibrational state of this stretching mode during the desorption process. We described the desorption dynamics by using the time propagation of the density matrix. The effects of vibrational relaxation were included by using a Redfield-type model. We also investigated the validity of the parameters for dynamical calculations by ab initio methods. As a result, we obtained physically reasonable results for the desorption probability, mean translational energy, and vibrational state distribution for the desorbed NO molecules. (C) 2003 American Institute of Physics.