The compressive deformation of metallic glass Cu was studied under uniformly distributed strains with different rates at 1 K temperature using molecular dynamics simulations. The interaction between atoms in the system adopts the embedded atom method (EAM) reported by Mishin. We found that MG Cu is an elastic/perfect plastic material and the Young modulus is about 50 Gpa with strain rates from 0.1ns-1 to 10 ns-1. At low strain rates the sample deforms inhomogeneously and the amorphous phase transforms continuously to a crystalline phase. It was observed that the nucleation, growth and mergence processes of crystalline are induced by stress. At high strain rates the system passes through plastic deformations homogeneously and keeps the amorphous structure. The higher flow stress occurs at higher strain with the strain rate increasing. The stress effect is an important factor that induces MG crystallization just like temperature effect. The relationship between characteristic nucleation rate and strain rate determines the different deformation mechanism of MG.