The VASP (Vienna Ab-initio Simulation Package) based on the density-functional theory (DFT) method combined with projector augmented wave (PAW) method is used to calculate the lattice parameters, band gap, density of states (DOS), and formation enthalpy of ZnCdO alloy by considering all the doping configurations. The calculation results indicate that the average parameters of wurtzite (wz) Zn1-xCdxO alloy, a and c, increase linearly, but the ratio of c/a does not change obviously with the increase of Cd content. With increasing Cd content, the band gap is reduced and the variation of band gap can be fitted by Eg(x)=3.28-5.04x+4.60x2, which is consistent with the experimental results. At a given Cd content, different doping configurations result in different Eg values, being one of the reasons of widening of the photoluminescence spectra of ZnCdO alloy. The DOS of wz-ZnCdO alloy in conduction band is shifted towards the lower energy side after Cd doping, causing the reduction of band gap. The reduction of band gap can be attributed to the contribution of 5s states of Cd. By comparing the formation enthalpy of wz-ZnCdO with those of zinc blende and rocksalt ZnCdO alloys, we find that the wurtzite phase of ZnCdO can coexist with zinc blende phase in the range of Cd content from 0.25 to 0.75 and will transit to the rocksalt phase at the Cd content of about 0.80.