Zn1-xMgxSeyTe1-y quaternary alloys are frown on ZnTe(001) substrates for the first time. The photoluminescence properties of ZnMgSeTe are characterized by strong excitonic luminescence intensity with a narrow linewidth that indicate the high crystal quality and the composition homogeneity. It is deduced that the composition homogeneity of the alloy is originated from the stable sticking coefficient of group-VI species and the exclusion of impurity diffusion from the substrate. Type-I band lineup in the ZnTe/ZnMgSeTe single quantum well is estimated from the narrow and strong exciton luminescence line of the quantum well, and the band offset in this heterostructure is estimated based on the photoluminesence, photoluminescence excitation, and reflectance results as 20 delta E-c:80 delta E-v.