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Single crystals of Zn$_x$Cu$_{1-x}$V$_2$O$_7$ system with doping concentration of 0.05 and 0.15 were grown by the vertical gradient freezing technique. The crystal structures were confirmed by means of x-ray diffraction to be the beta phase of copper pyrovanadate, $\beta$-Cu$_2$V$_2$O$_7$, when the Zn concentration was as low as 0.05, on the contrary to the previous studies on polycrystal samples. The Rietveld refinement on x-ray diffraction patterns showed that that lattice constant along crystallographic a-axis was slightly increased when the doping concentration was decreased from x = 0.15 to 0.05. A $\theta$-2$\theta$ scan confirmed that the natural cleaved facet is crystallographic a-axis with FWHM around (200) peak of 0.17(1)$^\circ$, suggesting a high quality of the obtained single crystals.