In the present work, the density functional theory (DFT) was performed for the investigation of the structural, electronic and optical properties of the Zn1-xCdxSeyTe1-y quaternary alloys using the full potential linearized augmented plane wave (FP-LAPW) method. For the calculations of the structural properties we have used the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA-PBEsol). On other hand, the electronic properties have been computed within the local density approximation (LDA) in adding to the Tran-Blaha modified Becker-Johnson (TB-mBJ) approach. Our results indicate that the lattice constant, as well as the bulk modulus and the energy gap for the Zn1-xCdxSeyTe1-y quaternary show almost linear variations on the concentration x (0.125≤x≤0.875). In addition, the simulated band structures for theZn1-xCdxSeyTe1-y quaternary exhibits a direct-gap for all concentrations. Moreover, low bowing parameters are observed. Also, some interesting optical properties such as dielectric constant, refractive index, extinction coefficient, absorption coefficient and reflectivity have been calculated by using the TB-mBJ method.  The results of our computations shows that theZn1-xCdxSeyTe1-y quaternary alloy is a promissing candidate for optoelectronic applications. It is noteworthy that the present work is the first theoretical study of the quaternary of interest using the FP-LAPW calculations.