Structural, electronic and optical properties of Cd1-xSrxO (0 \leq x \leq 1) are calculated for the first time using density functional theory. Our results show that these properties are strongly dependent on x. The bond between Cd and O is partially covalent and the covalent nature of the bond decreases as the concentration of Sr increases from 0 to 100%. It is found that Cd1-xSrxO is an indirect bandgap compound for the entire range of x and the bandgap of the alloy increases from 0.85 to 6.00 eV with the increase in Sr concentration. Frequency dependent dielectric functions ε1(ω), ε2(ω), refractive index n(ω) and absorption coefficient α(ω) are also calculated and discussed in details. The peak value of refractive indices shifts to higher energy regions with the increase in Sr. The striking feature of these alloys is that Cd0.5Sr0.5O is an anisotropic material. The larger value of the extraordinary refractive index confirms that the material is positive birefringence crystal. The present comprehensive theoretical study of the optoelectronic properties of the material predicts that it can be effectively used in optoelectronic applications in the wide range of spectrum; IR, visible and UV.