  Structure and magnetic properties of the compounds $Zn_{1-x}Cu_xCr_2O_4$
(ZCCO) are investigated systematically. A structural phase transition from
space-group symmetry $Fd3m$ to $I4_1/amd$ is observed in ZCCO. The critical
value of the doping, $x$, appears at $0.58\sim 0.62$ through the appearance of
a splitting of diffraction peaks at room temperature. Measurements of dc
magnetization, ac susceptibility, memory effect and exchange bias-like
(EB-like) effect have been performed to reveal the glassy magnetic behaviors of
ZCCO. The system with $x\leqslant 0.50$ is suggested as a spin glass-like
(SG-like) of magnetic characterization whereas doping values of $0.58\leqslant
x\leqslant 0.90$ defines the system as a $"$cluster glass-like$"$ (CG-like)
with unidirectional anisotropy. The Cu content suppresses the geometrical
frustration of $ZnCr_2O_4$, which may correlate with the pinning effect of Cu
sublattice on Cr sublattice to a preferential direction.
