Nuclear-grade zirconium alloys properties are very similar to those of pure zirconium (Zr), because in most cases they contain more than 95% of Zr atoms. They have extensive application in nuclear industry, especially in fuel cladding. Lattice properties of pure Zr and Zr-1%Nb alloy have been explored in this study. Point defect formation energies have also been calculated. Then, di-vacancies have been considered to check the cluster vacancy production. In the next section, the stability of niobium (with different size) clusters have been considered. Furthermore, assuming the Nb-cluster production, it has been shown that the niobium atoms binding energy in cluster form is positive that means the niobium atoms tend to make a cluster, when they bring near together. Finally, the effect of pressure on this clusterization has been studied. The results show that (except of cluster with 2 niobium atoms) the binding energy has been decreased with increasing pressure and therefore the clusters will be unstable.