We investigated magnetic properties of spinel oxides Zn (Cr1-xFex)2O4 to study element substitution effects on magnetism of spin-frustrated spinel oxides ZnCr2O4 and ZnFe2O4. The present study revealed that an antiferromagnetic order of ZnCr2O4 (TN ~ 13 K) is suppressed by Fe doping. Zn (Cr1-xFex)2O4 with x = 0.1, 0.5, and 0.7 exhibits spin-glass-like behavior below ~ 10 K. On the other hand, Zn (Cr1-xFex)2O4 with x = 0.3 exhibits the absence of magnetic order or spin-glass-like behavior down to low temperature (3 K), which is probably due to the competition of geometrical and bond frustrations.