The effect of uniaxial elastostatic compression on the deformation behavior of the Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 (Vit1) bulk metallic glass (BMG) was reported. The as-cast alloy was pre-compressed under various time (20, 40 and 60 h) at a preloading level of 87% of its yield strength. It was found that elastostatic compression can lead to structural rejuvenation or relaxation depending on the pre-compression time. Elastostatic compression, for 40 h, increased the free volume and improved the plasticity of the BMGs from 1.4% to 3.4%, but preloading for 60 h decreased the free volume and worsened the plasticity. In addition, the heterogeneous structure evolution during creep deformation has been analyzed by the Maxwell-Voigt model with two Kelvin units, revealing that more (less) defects with larger size are activated after elastostatic compression treatment for 40 h (60 h). This work sheds new light on the correlation between heterogeneous structure and plasticity/creep behaviors of Zr-based BMGs.