A single crystal of a new layered telluride KFeCuTe₂ has been successfully synthesized by the self-flux method, which is formed by intercalating K in the parent telluride Fe_1+xCuTe₂. This new compound crystallizes in the space group I4/mmm with the interstitial Fe in pristine Fe_1+xCuTe₂ completely removed after K intercalation. X-ray photoelectron spectroscopy (XPS) shows that after intercalation, the valence of Fe switched from a mixture of +2 and +3 to the single trivalent one. The KFeCuTe₂ is a Mott semiconductor (E_g = 1.06 eV) with a larger resistivity than that of Fe_1+xCuTe₂ due to the absence of electron doping from interstitial Fe atoms. Most importantly, the magnetic susceptibility shows the antiferromagnetic transition in KFeCuTe₂ at 60 K, instead of the spin-glass behavior in Fe_1+xCuTe₂, indicating the crucial role of interstitial Fe in breaking the long-range magnetic ordering. Our work provides a new compound to study the effect of interstitial Fe on the crystal and magnetic structure in layered tellurides.