In the field of machine learning (ML) and data science, it is meaningful to use the advantages of ML to create reliable interatomic potentials. Deep potential molecular dynamics (DEEPMD) are one of the most useful methods to create interatomic potentials. Among ceramic materials, amorphous silicon nitride (SiNx) features good electrical insulation, abrasion resistance, and mechanical strength, which is widely applied in industries. In our work, a neural network potential (NNP) for SiNx was created based on DEEPMD, and the NNP is confirmed to be applicable to the SiNx model. The tensile tests were simulated to compare the mechanical properties of SiNx with different compositions based on the molecular dynamic method coupled with NNP. Among these SiNx, Si3N4 has the largest elastic modulus (E) and yield stress (σs), showing the desired mechanical strength owing to the largest coordination numbers (CN) and radial distribution function (RDF). The RDFs and CNs decrease with the increase of x; meanwhile, E and σs of SiNx decrease when the proportion of Si increases. It can be concluded that the ratio of nitrogen to silicon can reflect the RDFs and CNs in micro level and macro mechanical properties of SiNx to a large extent.