In the process of nuclear waste disposal, the valuable uranium and plutonium are recycled and separated by dissolving the spent fuel in nitric acid. However, transuranic Np greatly influences the process of separation and recovery. Therefore, it is vital to study the structure and properties of nitrate, which is combined with neptunium ions and nitric acid. Furthermore, there are few researches about nitrate formed by tetravalent neptunium ions. So in this article, by using B3LYP hybrid method of density functional theory, the Gaussian 03 program is used to optimize the geometric construction of the coordination compounds Np(NO3)nq (n=1-6, q=-2-+3) formed by the tetravalent neptunium ions (Np4+) and nitrate ion (NO3-). Under the relativistic effective core potential model, the structure parameters and properties are reported. It is found that NO3- coordinates to Np4+ as a bidentate ligand, and the NpN and NpO bonds are the shortest in Np(NO3)22+, while the binding energy of the Np(NO3)4 is the largest. The infrared spectra of Np(NO3)4 are calculated in the gas and liquid phase. Comparing with the available experimental data, the reliability of the calculation results in this work is confirmed.