We constructed a new, accurate twelve-dimensional potential energy surface (PES) for ammonia dissociative chemisorption (DC) on a rigid Fe(111) surface using the fundamental invariant-neural network fitting to a large number of density functional theory data points. The DC dynamics simulations were carried out by the quasi-classical trajectory (QCT) approach. At very low collision energies, the molecules experienced a large number of rebounds due to the deep pre-transition-state adsorption well and finally decomposed around the global transition state. At high collision energies, the bridge site with a loose transition state was the most favorable site for dissociation. The mode-specific dynamics revealed that excitations in symmetric stretch and umbrella modes were most efficient in promoting the dissociation and were more efficacious than the same amount of translational energy. The computed large dissociation probability for NH3/Fe(111) supported the fact that iron is an effective catalyst for ammonia dissociation, which is of practical importance in producing clean hydrogen.