In this paper, a theoretical study of calculating Compton profiles(CPs) for β-Zr using the renormalized-free-atom model and free electron model for different configurations (4d3-x-5s1+x),where (x= 0.1 to 1 step 0.1) is presented .The theoretical results and previously experimental data show good agreement and the best electronic configuration found was (4d2.8-5s1.2 ). The cohesive energy of β-Zr is computed by using theoretical Compton profile data and compared with available data. The band structure and density of state of (β-Zr and -Zr) phases are determined from density functional theory (DFT) with use Quantum wise Atomistix Tool Kit (ATK),Virtual Nano Lab calculations within the framework of the local density approximation (LDA).