Three incongruent melting LawNdxGdyYzSc4-w-x-y-z(BO3)4 (LGYSB:Nd) crystals with different Y concentrations (z = 0.15, 0.05, and 0.025) have been grown by the Czochralski method for the first time. The LGYSB:Nd-type crystals exhibit an acentric structure similar to that of the natural mineral huntite CaMg3(CO3)4, with space group R32. The composition of the LGYSB:Nd_3 (z = 0.025) crystal grown from the starting melt composition La0.628Gd0.547Y0.025Nd0.05Sc2.75(BO3)4 was measured by inductively coupled plasma mass spectrometry method, and it was found to be La0.6794Gd0.4105Y0.0178Nd0.0381Sc2.8542(BO3)4. The transversal spatial distribution of the refractive index in the LGYSB:Nd_3 crystal was investigated. Third-order nonlinear optical susceptibility χ(3) of the LGYSB:Nd_3 crystal was determined from third-harmonic generation experiments with ultrashort (fs) laser pulses. The optical transmission spectrum was measured in the range of 200-2000 nm. The absorption cross-section at 808 nm in σ-polarization was determined to be 1.18 × 10-19 cm2 for the LGYSB:Nd_3 crystal. The 10K absorption spectra revealed that the Nd3+ ions occupy only La3+ cationic sites in the LGYSB host matrix. The emission cross-section at 1064 nm in σ-polarization was determined to be σem(σ) = 1.74 × 10-19 cm2 for the LGYSB:Nd_3 crystal. The fluorescence lifetime was found to be τ = 115 μs for all of the LGYSB:Nd crystals. The LGYSB:Nd_3 laser was operated at an emission wavelength of 1062 nm with very high slope efficiencies of ηsa = 0.74 and ηsa = 0.64 in quasi-cw and cw regimes, respectively.