The investigation of the quantum effect for the dissociative chemisorption dynamics is an important subject. Recent studies revealed significant quantum effects for the heavy-diatomic reaction of N 2 + Fe( 111), but it is still uncertain how extensive the quantum effects are in the heavy-atomic molecule dissociation on surfaces. Here, six-dimensional (6D) quantum dynamics and quasiclassical trajectory (QCT) calculations were carried out for the NO + Cu(111) reaction, based on the newly developed 6D potential energy surface (PES) by neural network (NN) fitting. The comparisons made between quantum and quasi-classical dissociation probabilities reveal a weak quantum effect in this reaction. The effects of incidence energy, rovibrational excitations, and the incidence angle of the NO on the reactivity were investigated. The vibrational excitation can efficiently facilitate the dissociation, which agrees well with the experimental results. Moreover, the vibrational excitation is more efficient than the same amount of translational energy in facilitating the reactivity of NO on Cu(111), which may be attributed to dynamical effects, such as the bobsled effect and the typical late barrier for this reaction.