In this letter, Nd:Ca4Gd0.275Y0.725 O(BO3)(3) (Nd:GdYCOB) single crystal with good optical quality and large size has been grown by the Czochralski method. The absorption and fluorescence spectra have been measured. The self-frequency doubling (SFD) laser output of Nd:GdYCOB at 0.53 mu m has been demonstrated when a Nd:GdYCOB crystal sample with dimensions of 3 mm x 3 mm x 7 mm (the phase-matched angle is theta = 78.8 degrees, phi = 90 degrees) is pumped by a cw Ti:sapphire laser.