We have calculated structures and energies for the hydrogen-bonded complexes of tri-n-butyl phosphate with nitric acids and water molecules, which might have crucial role in the PUREX process for the reprocessing of spent nuclear fuel and the treatment of nuclear wastes in the nuclear industry. The structure and H-bond strengths for the TMP-(HNO3)(x)(H2O)(y), complexes with x + y = 1-3 have been calculated. Short and strong hydrogen bonds are formed between phosphoryl oxygen and the proton of nitric acid. The hydrogen bonds between water and the phosphoryl oxygen are weaker and longer. The more H-bond donors are bound to the phosphoryl oxygen, the weaker and the longer H-bonds become. Weak hydrogen bonds between methyl and water might contribute to the stability of the clusters. Solvent effect seems very important to the relative stability of complexes. We have calculated the solvation free energies of TMP complexes using the dielectric continuum approach in order to model the solvent effect of tri-n-butyl phosphate and supercritical-CO2 approximately. The TMP-(HNO3)(H2O)(2) and TMP(HNO3)(2)(H2O)(II) are two most stable complexes, which agree well with experimental results.