A new passively self-Q-switched Nd, Cr:GdVO(4) laser crystal was grown by Czochralski method for the first time to our knowledge. Polarized absorption spectra were measured at room temperature. The absorption bands display polarization character and an absorption band of Cr(5+) ions at 1110 nm enables the crystal to be a self-Q-switched laser material at 1.06 mum. In the passive self-Q-switching operation, the maximum output power, shortest pulse width, and largest pulse energy were obtained to be 265 mW, 230 ns, and 1.12 microJ, respectively.