Polynitrogen clusters are of great interest as potential high-energy-density materials (HEDMs). However, it is still a challenge to effectively manufacture pure nitrogen clusters. Here, we present a method to produce all-nitrogen clusters ranging in size from 3 to 10 using a self-developed apparatus consisting of a laser vaporization cluster source and a mass spectrometer. The results indicate that the mass peak of the N4+ cluster is dominant, and the cooling of the cluster source with liquid nitrogen effectively enhanced the intensities of larger nitrogen clusters. The trace amounts of water in the carrier gas affects the relative signal intensities of nitrogen clusters, suggesting that water molecules can affect their stabilities. The geometrical structures of the Nn+/0 (n=3-10) clusters are determined by CALYPSO cluster structural search method and density functional theory calculations. A series of promising polynitrogen clusters, such as Z-shaped N4+/0 clusters and bicyclic N8+/0 clusters, are identified. The molecular dynamics simulations indicate the decomposition energy barrier of (N4-H2O)+ cluster is lower than that of N4+cluster by 2.3 kcal mol-1, while the decomposition energy barrier of (N8-H2O)+ cluster is higher than that of N8+ cluster by 1.4 kcal mol-1. These findings provide useful information for the generation and stabilization of polynitrogen clusters, which are valuable for the design and synthesis of HEDMs.