A Cr3+/Nd3+ co-doped calcium tantalum gallium garnet (Cr3+:Nd3+:CTGG) crystal with dimensions of Phi 20 mm x 40 mm was successfully grown for the first time by the Czochralski method. X-ray powder diffraction pattern of Cr3+:Nd3+:CTGG was given out. The structure parameters were calculated and still belong to the cubic system. The thermal expansion and specific heat were evaluated, the absorption spectra and fluorescence spectra at room temperature were also investigated, the Cr3+ acted as a sensitizer in this crystal for energy transfer. The laser output at 1.064 mu m was performed which was pumped by a xenon lamp pump.