Nd3+-doped calcium niobium gallium garnet single crystal fibers (Nd:CNGG SCFs) with varying Nd3+ concentrations were successfully grown using the laser-heated pedestal growth (LHPG) method. The study thoroughly examines the fundamental physical structure, optical properties, and laser characteristics of the as-grown Nd:CNGG SCFs. Results indicate that the Nd:CNGG SCF exhibits broader absorption and emission full width at half maximum (FWHM) compared to bulk single crystals. Moreover, pumped by a commercial 808 nm laser diode, continuous-wave laser operation at 1061 nm with a half-height width of 1.86 nm was achieved. The laser output power reached 1.04 W at an absorbed power of 7.46 W, with a slope efficiency of 25.4% relative to the absorbed pump power. These findings suggest that Nd:CNGG SCF holds promise as a practical and potent candidate for laser gain medium, offering significant research potential in the field of lasers.