An eutectic LiCl/KCl flux method in a horizontal configuration has been used to grow a series of homogeneous Fe1+δSe1-xTex single crystals of high quality with 0.5 ≤ x ≤ 1. Compared with previously used melt-growth method, the stable crystallization process in LiCl/KCl flux below their peritectic temperatures results in better homogeneity and crystalline perfection identified by energy dispersive spectrometer and x-ray diffraction. The interstitial Fe value δ remains small within 0.5 ≤ x ≤ 0.85 where the superconducting temperature TC is not sensitive to the Te content with sharp superconducting transition widths ΔTC < 1 K and a maximum of TC = 14.3 K at x = 0.61. The value δ starts to increase quickly accompanied by a deviation of linear behavior of crystal lattice parameters as well as the broadening of ΔTC = 2.1 K at x = 0.91, then suddenly rises up to δ > 0.1 followed by the disappearance of superconductivity and emergence of antiferromagnetic order at x ≥ 0.96. We also observed a metallic to semiconducting transition in the normal state resistivity of Fe1+δSe1-xTex with increasing Te content which is related to a localized electronic state induced by the interstitial Fe. The interstitial Fe value δ might be a key physical parameter to understand various properties of Fe1+δSe1-xTex system.