YbxY1-xAl3(BO3)(4) (x = 0.1, 0.07 and 0) crystals have been grown by the flux method. The growth defects of YbxY1-xAl3(BO3)(4) crystals were detected by X-ray topography. It is found that the perfection of YbYAB crystal with low Yb dopant is better than that with high Yb dopant. In Yb0.1Y0.9Al3(BO3)(4) crystal, growth bands, growth boundaries, grown-in dislocations and inclusions were observed. However, the densities of growth defects for Yb0.07Y0.93Al3(BO3)(4) and YAl3(BO3)(4) are low and no obvious inclusions are observed in these crystals. In addition, growth twins were detected in YbxY1-xAl3(BO3)(4) crystal by using the chemical etching method. It is found that the growth twins occur frequently in Yb0.1Y0.9Al3(BO3)(4) crystal whereas no growth twin appears in YAl3(BO3)(4) crystal. Based on the experimental observations, the formation mechanism of growth twins is discussed. In the meantime, the effective measures for reducing the growth twins and defects are proposed.