We report the growth of a Nd-doped calcium barium niobate (Nd:CBN-28) single crystal using the Czochralski method. The point group and space group of Nd:CBN-28 are determined to be tetragonal 4mm and P4bm, respectively, and the effective segregation coefficients of Nd, Ca, Ba, and Nb are 0.988, 1.029, 0.992, and 0.985, respectively. The density of the material is 5.321 g cm−3 at 19.6 °C, in good agreement with the theoretical value. Thermal expansion measurements reveal that during the heating cycle, the c-axis of Nd:CBN-28 undergoes both thermal contraction and thermal expansion, while at the same time there is only expansion along the a-axis. Specific heat measurements reveal that an anomaly appears at about 220 °C due to a phase transition. The thermal diffusivity increases slowly with increasing temperature. The thermal conductivity of the crystal has been calculated from these results, and the phonon mean free paths la and lc along the a- and c-axes of Nd:CBN-28 crystal are estimated. The transmission spectrum of Nd:CBN-28 crystal along the [001] direction has been measured.