Pure and Nd-doped Ca$_{10}$Li(VO$_{4}$)$_{7}$ single crystals were grown by the Czochralski method. The structure of Ca$_{10}$Li(VO$_{4}$)$_{7}$ single crystal was refined starting from a model of Ca$_{10}$K(VO$_{4}$)$_{7}$ using the powder diffraction data collected at a laboratory high-resolution diffractometer. The defect structure of the single crystal was studied with the use of both, high-resolution diffraction using a laboratory instrument and X-ray topographic techniques employing synchrotron radiation at the Hasylab laboratory (Hamburg). Polarized absorption and luminescence spectra of Nd-doped Ca$_{10}$Li(VO$_{4}$)$_{7}$ crystal were investigated in details. The laser oscillation was obtained under flash lamp pumping and the slope efficiency of 0.87% was achieved in the free-running mode. Preliminary examination of lasing properties points that Ca$_{10}$Li(VO$_{4}$)$_{7}$:Nd crystal can be a highly efficient solid state laser medium. Crystals of this kind are expected to be suitable for application as efficient non-linear optics materials.