We report that beta'-Gd-2(MoO4)(3) crystals have been grown by the Czochralski (CZ) method. We studied the growth conditions of beta'-Gd-2(MoO4)(3) crystal. A comparison between the resistance-heated method and radio frequency induction-heated method is described. Also, the in situ observation of the domain structure by the microscope and by synchrotron radiation X-ray topography under the conditions of DC polarization voltage and temperature change were carried out. Experiments showed that multidomain structure including ferroelectric and ferroelastic domains occurred in beta'-Gd-2(MoO4)(3) crystal. Usually ferroelectric domains appeared in the as-grown crystal and ferroelastic domains appeared in the polished thinner piece. Both ferroelectric and ferroelastic domains disappeared when the temperature of the crystal piece was higher than the Curie temperature T-C and they could be reproduced when the temperature of the crystal piece was lowered below Tc. When a DC polarization voltage ranging from 150 to 500 V was applied on a c-axis beta'-Gd-2(MoO4)(3) piece having a thickness of 0.5 mm, the multidomain would gradually transform to a single domain. This result means that it is possible to make a periodically poled beta'-Gd-2(MoO4)(3) crystal.