Molecular dynamics simulations were carried out to investigate the atomic structure of a model Cu64Zr36 bulk metallic glass (BMG). It is found that the amount of icosahedral content of the system is significantly increased in a well relaxed structure. While we considered four connection types of vertex-, edge-, face-, and volume-sharing, the huge cluster in the relaxed samples mainly involve volume-type connection and exhibits a remarkable athermal plasticity that great stiffness and great yield strength compared to the as-quenched samples. In addition, the bond-angle distribution of annealed sample shows sharp peaks at specific bond angles which is an evidence of crystallized Laves-phase formed by icosahedral atoms, however the peaks are to be broaden after loading, which indicates decreasing amount of icosahedral content and their shape distortion. These results suggest that icosahedral content in a bulk metallic glasses plays a key role to determine the mechanical properties such as rigidity and maximum stress carrying capacity.